Evaluate the infinite series:
[tex] \displaystyle \large{ \sum_{n = 1}^{ \infty} \frac{1}{(n + 1) \sqrt{n} + n \sqrt{n + 1} } }[/tex]
Please show your work too — thanks!

Answers

Answer 1

9514 1404 393

Answer:

sum = 1

Step-by-step explanation:

The method of partial sums has you look at sums of various numbers of terms of the series to see if there is a pattern that suggests either divergence or a limit. Here, the partial sums suggest the series sum is 1.

In the attachment, we have computed sums of 1 term, 10 terms, 100 terms, and so on up to 10^8 terms. These sums seem to approach the value 1.

Individual terms get small faster than for a harmonic series, which his known not to converge, but more slowly than a quadratic series. Large numbered terms are approximately proportional to n^-(3/2).

_____

You can actually compute the sum exactly, without reference to partial sums. Each term of the sum can be rewritten as ...

[tex]\dfrac{1}{(n+1)\sqrt{n}+n\sqrt{n+1}}=\dfrac{1}{\sqrt{n(n+1)}(\sqrt{n+1}+\sqrt{n})}\\\\=\dfrac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n(n+1)}}=\dfrac{1}{\sqrt{n}}-\dfrac{1}{\sqrt{n+1}}[/tex]

Then successive terms will cancel the intermediate fractions. So, for example, the sum of the first 3 terms is ...

(1/√1 -1/√2) +(1/√2 -1/√3) +(1/√3 -1/√4) = 1 -1/√4

This means the given sum will evaluate to ...

1 -1/√∞ = 1 -0 = 1 . . . sum of the infinite series

$Evaluate The Infinite Series:[tex] \displaystyle \large{ \sum_{n = 1}^{ \infty} \frac{1}{(n + 1) \sqrt{n}$

Related Questions

Please help me in this:

Answers

Answer:

;sjjdje

Step-by-step explanation:

4djdeje

if tanA/2=4/3, find The value of sinA, cosA

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given :- tanA=4/3

we already know that tanA=P/B

From Pythagorean theorem we get..

H²=P²+B²

H²=4²+3²

H²=16+9

H²=25

H²=5²

H=5

SinA=P/H

CosA=B/H

from that

SinA= 4/5

CosA=3/5

help ill give brainly

Answers

Answer:

The answer would be 26%

Step-by-step explanation:

Answer:27

i think that 27 is the answer

least common denominator between the fractions 1/3 and 2/8

Answers

Answer:

LCD 1

Step-by-step explanation:

Answer:

I believe the LCD is 24.

Step-by-step explanation:

Denzel identified (3,2) as a point on the line y-2 = 2/3 (x+ 3). What is the error Denzel made?

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Hi there!

»»————-　★　————-««

I believe your answer is:

He identified the incorrect x-value.

See explanation below.

»»————-　★　————-««

Here’s why:

⸻⸻⸻⸻

[tex]\text{General Point-Slope Form is:}\\\\y - y_1 = m(x-x_1)\\\rule{150}{0.5}\\\\(x_1,y_1) -\text{A point that is given.}\\\\m -\text{Slope}[/tex]

⸻⸻⸻⸻

Denzel incorrectly identified the x-value of the given point. The value '-3' is actually indicated in the equation. If you plug in '-3' into the equation, you would get '-(-3)', which simplifies to '+3'.

⸻⸻⸻⸻

[tex]y-2 = \frac{2}{3} (x-x_1)\rightarrow y-2 = \frac{2}{3} (x-(-3))\rightarrow y-2=\frac{2}{3} (x+3)[/tex]

⸻⸻⸻⸻

The point in the equation should be: (-3, 2).

»»————-　★　————-««

Hope this helps you. I apologize if it’s incorrect.

The correct points of the line will be (-3,2).

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the point (3,2) is on the line y-2 = 2/3(x+ 3). Satisfy the equation with the given point and check.

y-2 = 2/3(x+ 3)

2-2 = (2/3)(3 + 3)

0 = 4

To make left hand side and right hand side equal the value of x coordinate should be -3.

y-2 = 2/3(x+ 3)

2-2 = (2/3)(3 + 3)

0 = 0

Therefore, the correct points of the line will be (-3,2).

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step by step explanation of
((3^-1)^-2 -2^3)^-1

Answers

Answer:

SEARCH MO PARA MALAMAN MO HEHE

Someone pls help me I will make you brain

Answers

Answer: -75

Step-by-step explanation:Because basically the slope is how much money is going down in the loan so 850 minus 75 is 775 so -75 is the answer

-75 is the correct answer i hope i helped you out so i hope i can get brainlist :)

Find m Give explanation please

Answers

Answer:

m < FGN = 88°

Step-by-step explanation:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).

Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:

The following equality statement can be established according to the exterior angle theorem:

m < E + m < F = m <FGN

38 + 6x - 10 = 7x + 18

Combine like terms:

28 + 6x = 7x + 18

Subtract 6x from both sides:

28 + 6x - 6x = 7x - 6x + 18

28 = x + 18

Subtract 18 from both sides:

28 - 18 = x + 18 - 18

10 = x

Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.

m < E + m < F = m <FGN

38° + (6x - 10)° = (7x + 18)°

38 + 6(10) - 10 = 7(10) + 18

38 + 60 - 10 = 70 + 18

88 = 88 (True statement).

Therefore, m < FGN = 88°

please help me to solve problems

Answers

Step-by-step explanation:

4a)

the principle of similar triangles : they have the same angles.

and we do not forget : the sum of all angles in a triangle is always 180 degrees.

a = 180 - 65 - 45 = 70 degrees

b = 65 degrees

c = 70 degrees

same principles.

x = 58 degrees

y = 52 degrees

z = 180 - 58 - 52 = 70 degrees

same principles.

plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.

x = 85 degrees

y = 180 - 40 - 85 = 55 degrees

z = 180 - 85 = 95 degrees

again same principles.

y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).

the angle POQ is again complementary with 87 degrees,

POQ = 180 - 87 = 93 degrees

x + y + 93 = x + 2x + 93 = 180

3x = 87

x = 29 degrees

y = 2x = 2×29 = 58 degrees

please solve fast it's urgent

Answers

Answer:

∅=30°

Step-by-step explanation:

[tex]sin[/tex]∅[tex]=\frac{1}{\sqrt{3} }sin60^{0}[/tex]

sin∅=[tex]\frac{\frac{\sqrt{3} }{2} }{\sqrt{3} } =\frac{\sqrt{3} }{2\sqrt{3} }=\frac{1}{2}[/tex]

∅=[tex]sin^{-1}(\frac{1}{2})= 30^{0}[/tex]

I hope this help you

helppppppppppppppppppppppppppppppppppppppmeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

wheeeeeeeeeeeeere is theeeeeeeeeeee queeeeeeeeeestion?

Given below is an equation of a parabola. What are the coordinates of the vertex?
y = (x + 2)^2

a (–2, 0)
b (2, –2)
c (–2, 2)
d (2, 0)

Answers

a (-2,0) is correct; enter into graphing calc or solve algebraically

The product –2 • (–5) is shown on the number line. A number line shows an arrow from 0 to negative 5 labeled negative 5, another arrow from negative 5 to negative 10 labeled negative 5, and another arrow from 0 to 10 labeled the opposite of 2 times negative 5. Complete the sentences to explain how the model on the number line could be used to find the answer. Starting at 0 move twice to the left______ spaces. 2 • (–5) = ______. The answer is the opposite of that value, ______ .

Answers

Answer:

Starting at 0 move twice to the left___5___ spaces. 2 • (–5) = ___-10___. The answer is the opposite of that value, ___10___ .

Step-by-step explanation:

The required blank space is filled by the numbers, 5, -10, and 10.

Given that,
Starting at 0 move twice to the left______ spaces. 2 • (–5) = ______. The answer is the opposite of that value, ______ . To determine the solutions for the blank spaces.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

here,
The number line 2(-5), shows that move twice to the left 5 spaces.
And This results in -10 spaces having to move, and the outcome is the opposite of the number 10.

Thus, A complete solution is "Starting at 0 move twice to the left 5 spaces. 2 • (–5) = -10. The answer is the opposite of that value, 10.

Learn more about number line here:

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-343 as a power of (-7)

Answers

Answer:

[tex]-342^{-7}[/tex]

Step-by-step explanation:

If we represent 343 as a power of (-7)

we get [tex]-342^{-7}[/tex]

the equation will be this

= -347 × -347 × -347 × -347 × -347 × -347 × -347

solve equation s - 12= 20. s=?

Answers

Answer:

s = 32

Step-by-step explanation:

We have our equation:

s - 12 = 20

And we are trying to find s. Therefore, we can isolate the variable s, which means we have to move all the values from the variables side to the other side, like so:

s - 12 = 20

+12 +12 (we add 12 to both sides in order to cancel out the -12, and also because whatever we do to one side, you have to do to the other!)

So, now our equation will look like this:

s = 20 + 12,

or,

s = 32

Which happens to be our answer!

Hope this helps :)

How do you solve y=3x²-6x-1 using completing the square?

Answers

(B/2)^2 is the formula you need to complete the square
B is the second term which is -6
So let’s plug it into the formula
(-6/2)^2
(-3)^2= 9

Select the shapes that are similar to shape A

Answers

Answer:

purple in the top left

Step-by-step explanation:

um I don't know, it looks right, lol I'm sorry I hope this helps you let me know if its right

i think it is the pink one that is similar to A

In a classroom,
1/6
of the students are wearing blue shirts, and
2/3
are wearing white shirts. There are 12 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts

Answers

Answer:

There’s 2 students not wearing blue or white shirts.

Step-by-step explanation:

Solve by multiplying
digits of value and filling
in zeros:
700 x 102
Х
HELP PLEASE

Answers

the answer is 70,000

10x + 6 - 2x - 20 Question 1 options:

12x + 26

8x + 26

8x - 14

12x + 14

---------------------------------

5x2 + 3 + 3x + x2 – 1

Question 2 options:

6x2 + 3x + 2

9x2 + 2

8x2 + 2

6x2 + 3x + 4

--------------------

(x−13)(x7)(x3)

Question 3 options:

x−10

1x3

x273

x−273

---------------------

(2xy)3

Question 4 options:

2x3y3

8x3y3

6x3y3

6xy

---------------------

xy−5

Question 5 options:

y5x

5xy

xy5

xy5

-----------------------

10x6x2

Question 6 options:

10x8

x4

10x4

(10x)4

----------------------

Evaluate

50⋅ 54

------------

53

Question 7 options:

Solve proble

Answers

Step-by-step explanation:

10-2x + 6- 20

8x-14 the answer of first question

. Given g(x) = -x2 + 10x - 3, find the following. explain it pls pls

Answers

Answer:

The value of g(x) at x=-3 is -42

That is g(-3)=-42

Step-by-step explanation:

Given that the function g is defined by

To find the value of g(-3) :

That is to find the value of g(x) at x=-3 :

Put x=-3 in the above function we get

Therefore g(-3)=-42

The value of g(x) at x=-3 is -42

That is g(-3)=-42

What is the product?
(3x-6)(2x2-7x+1)
0 -12x2+42x-6
0-12X2 +21x+6
6x3-33x2+45x-6
O 6x3 - 27x2-39x+6

Answers

Answer6x3-33x2+45x-6

Step-by-step explanation:

The product of polynomials is 6x³-33x²+45x-6. Therefore, option C is the correct answer.

What is product of polynomials?

To multiply two polynomials: multiply each term in one polynomial by each term in the other polynomial. Add those answers together, and simplify if needed.

Given that, (3x-6)(2x²-7x+1).

By using distributive property, we get

3x(2x²-7x+1)-6(2x²-7x+1)

= 6x³-21x²+3x-12x²+42x-6

= 6x³-21x²-12x²+3x+42x-6

= 6x³-33x²+45x-6

Therefore, option C is the correct answer.

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Mathematics Ratio
Help plz

Answers

Answer:

480

Step-by-step explanation:

Check out the solution

Find the value of x in the triangle shown below.

a)=5

b)x=\/7
c)x = 7
d)x = 25

Answers

C. x = 7 that is the answer

I need help understanding how to do this. I can understand the basic idea, I just don't know how to work with letters very well.

Answers

Answer:

(etr)^3 , 70f^6g^2h

Step-by-step explanation:

e^2r^2t^3

e^3r^3t^2

LCM=e^3r^3t^3

(etr)^3

10f^2gh

35f^3g^2

LCM= 70f^3g^2h

Please Help Me

The ratio of the number of combinations (2n+2) of different objects taken n at a time to the number of combinations of (2n-2) of different objects taken n at a time is 99:7. Find the value of n.

Answers

The expected value of n is 1.152

The question states that ratio of 2n+2 and 2n-2 = 99:7. This means that

2n+2:2n-2 = 99:7, this also means that

[tex]\frac{2n+2}{2n-2}[/tex] = [tex]\frac{99}{7}[/tex]

If that is so, we can cross multiply so that

99 * (2n - 2) = 7 * (2n + 2), on expanding the bracket, we have

198n - 198 = 14n + 14

198n - 14n = 14 + 198

184n = 212, dividing both sides by 184, we have

n = 212/184

n = 1.152

Therefore, the value of n is 1.152

Read more here https://brainly.com/question/11018135

Use the remainder theorem to determine whether x=-4 is a solution of
[tex] {x}^{6} + {5x}^{5} + {5x}^{4} + {5x}^{3} + {2x}^{2} - 10x - 8[/tex]

Answers

Answer:

The remainder is zero. Then x = –4 is a solution of the given equation.

Hello haohaoxNienie!

[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

Use the remainder theorem to determine whether x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]

Refer to the attached picture.

Steps :-First find the divisor using the given information (x = - 4).Now, divide x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8 by x + 4.We'll get the remainder as 0.Using the remainder theorem & solving it, we'll get LHS & RHS as 0.Hence proved.

Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

__________________

Hope it'll help you!

ℓu¢αzz ッ

8 to the second power.(2+6) divided by 4=

Answers

i'm a little confused on the format but if you mean 8^2(2+6)/4 then the answer is 128

8x8 is 64, 64x8 is 512. 512/4 is 128

The value of given numerical expression is 128.

The given numerical expression is [8²×(2+6)]/4.

What is the exponent?

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

Now, the given expression can be solved as follows:

[8²×(2+6)]/4

= (64×8)/4

= 64×2

= 128

Therefore, the value of given numerical expression is 128.

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answer this pleaseeeeee ill give brainliest What is an equation of the line that passes through the points (-6, 3) and (-5, 2)?

Answers

Answer:

y-3=-1(x+6)

Step-by-step explanation:

I gotchu

brainliest tho?

f(x) = -x^2-3x
find f (10)

Answers

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

f*(x)-(-x^2-3*x)=0

STEP

Pulling out like terms

2.1 Pull out like factors :

fx + x2 + 3x = x • (f + x + 3)

Equation at the end of step

x • (f + x + 3) = 0

STEP

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : x = 0

Solution is x = 0

Equation of a Straight Line

3.3 Solve f+x+3 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line f+x+3 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of f is -3/1 so this line "cuts" the f axis at f=-3.00000

f-intercept = -3/1 = -3.00000

Calculate the X-Intercept :

When f = 0 the value of x is -3/1 Our line therefore "cuts" the x axis at x=-3.00000

x-intercept = -3/1 = -3.00000

Calculate the Slope :

Slope is defined as the change in f divided by the change in x. We note that for x=0, the value of f is -3.000 and for x=2.000, the value of f is -5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -5.000 - (-3.000) = -2.000 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -2.000/2.000 = -1.000

Geometric figure: Straight Line

Slope = -2.000/2.000 = -1.000

x-intercept = -3/1 = -3.00000

f-intercept = -3/1 = -3.00000

x = 0

Other Questions

Evaluate the infinite series:[tex] \displaystyle \large{ \sum_{n = 1}^{ \infty} \frac{1}{(n + 1) \sqrt{n} + n \sqrt{n + 1} } }[/tex]Please show your work too — thanks!​

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Evaluate the infinite series:
[tex] \displaystyle \large{ \sum_{n = 1}^{ \infty} \frac{1}{(n + 1) \sqrt{n} + n \sqrt{n + 1} } }[/tex]
Please show your work too — thanks!