use the integral test to determine whether the sum converges. [infinity] n = 1 1 n 9 evaluate the following integral. [infinity] 1 x 9 dx 1

Answers

Answer 1

The sum ∑ from n = 1 to infinity of 1/n^9 converges.

We will use the integral test to determine whether the sum converges.

To use the integral test, we need to evaluate the following integral:

∫ from 1 to infinity of 1/x^9 dx

We can integrate this using the power rule of integration:

= [-1/(8x^8)] from 1 to infinity

= [-1/(8 x infinity^8)] - [-1/(8 x 1^8)]

= 0 + 1/8

= 1/8

So, the integral converges to 1/8.

According to the integral test, if the integral converges, then the sum also converges. If the integral diverges, then the sum also diverges. Since the integral converges to a finite value of 1/8, the sum also converges.

The sum ∑ from n = 1 to infinity of 1/n^9 converges.

To know more about sum, visit;

https://brainly.com/question/24205483

#SPJ11


Related Questions

solve the system of equations
3x-3y=4
-3x+3y=3

Answers

Answer:

x=y+2/3

Step-by-step explanation:

I don't know I need help.
Which of the following numbers can be expressed as repeating decimals?

3 over 7, 2 over 5, 3 over 4, 2 over 9

2 over 9 and 3 over 4
3 over 7 and 2 over 5
2 over 5 and 3 over 4
3 over 7 and 2 over 9

Answers

Answer:

2/9 = 0.2 repeating

3/7 = 0.428571 repeating

Step-by-step explanation:

Please help

The figure

Answers

pentagonal prism

hope it helps you

Answer:

the last one

Step-by-step explanation:

because they are given their names based on their bases

Name the like terms
5a, 3, 4d , 2a, 2a, 5c

Answers

Answer:

"Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.

Step-by-step explanation: Hope this helps

Four friends go out to lunch together. Mike orders a personal pizza with 2 toppings for $7.00. Dustin orders a personal pizza with 5 toppings for $9.25. Lucas orders a calzone with 1 topping for $5.75. Will orders a calzone with 4 toppings for $8.75. For what number of toppings is the price of a personal pizza the same as a calzone?

Answers

Answer:

Step-by-step explanation:

Four friends go out to lunch together.

For what number of toppings is the price of a personal pizza the same as a calzone?

Let us represent the number of toppings as x

We need to know the price of a personal pizza and the price of a calzone

Mike orders a personal pizza with 2 toppings for $7.00.

2x = $7

x = $7/2

x = $3.50

Dustin orders a personal pizza with 5 toppings for $9.25.

5x = $9.25

x = $9.25/5

x = $1.85

Lucas orders a calzone with 1 topping for $5.75.

x = $5.75

Will orders a calzone with 4 toppings for $8.75.

4x = 8.75

x = 8.75/4

x =2.1875

i dont understand this

Find the slope of the linear function
y=5/4x-9​

Answers

Answer:

[tex]\frac{5}{4} x[/tex]

Step-by-step explanation:

y = mx+ b

m = slope

b = y-intercept

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the straight lines.

The equation of a straight line is given as,

y = mx+c, hence here, m = slope, c = y-intercept..

so, y = 5/4x-9

.m = 5/4

so the slope is 5/4

Triangle WXY is similar to triangle RST.
AA.
Which transformations could transform triangle WXY into triangle RST to show that they are similar?
Reflect across line PQ, then dilate with a scale factor greater than 1.
Reflect across line PQ, then dilate with a scale factor greater than 0 and less than 1.
Rotate 90 degrees counterclockwise about point P, then dilate with a scale factor greater than 1.
Rotate 180 degrees clockwise about point P, then dilate with a scale factor greater than 0 and less than 1.

Answers

Answer:

Reflect across the line PQ, then dilate with a scale factor greater than zero in less than one

Step-by-step explanation:

Answer:

Reflect across line PQ, then dilate with a scale factor greater than 0 and less than 1.

B

Step-by-step explanation:

With explanation please help

Answers

Answer:

first you simplify the first part which will be

(15)^2-(18+9)*(6)

225-27*6

225-162

Answer will be 63

I showed my work :)

Determine how many lines of symmetry each object has

Answers

i think the answer is zero

Johnny works after school and earns $8 per hour. He needs at least $2000 to purchase a car so he does not need to take the bus. How many hours does he need to work to reach his goal?​

Answers

2hours

Step-by-step explanation:

2 hours

Question:
What are the solutions to 3x^2 + 12x + 6 = 0?

Hint::
use the quadratic formula

Answers

Answer:

     x₁ = - 2 + √2 ,   x₂ = - 2 - √2

Step-by-step explanation:

[tex]3x^2 + 12x + 6 = 0\\\\a=3\,,\ b=12\,,\ c=6\\\\\\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\ x=\dfrac{-12\pm\sqrt{12^2-4\cdot3\cdot6}}{2\cdot3}=\dfrac{-12\pm\sqrt{144-72}}{2\cdot3}=\dfrac{-12\pm\sqrt{72}}{2\cdot3}=\dfrac{-12\pm6\sqrt{2}}{6}\\\\x_1=\dfrac{6(-2+\sqrt{2})}{6}=-2+\sqrt2\\\\x_2=\dfrac{6(-2-\sqrt{2})}{6}=-2-\sqrt2[/tex]

Circles A, B, and C overlap. x is in the overlap of circles A and B. Which of the following are true about x? Check all that apply. x ∉ A x ∈ B x ∉ C x ∈ A ⋃ B x ∈ A ⋃ C x ∈ A ⋂ B

Answers

9514 1404 393

Answer:

  b, c, d, e, f

Step-by-step explanation:

x ∉ A  . . . . .  not true, x is in A

x ∈ B . . . true

x ∉ C . . . true (x is outside the circle labeled C)

x ∈ A ⋃ B . . . true

x ∈ A ⋃ C . . . true

x ∈ A ⋂ B . . . true (x is in the overlap)

Answer:

A is false, every thing else is correct so b,c,d,e,f is your answer

Step-by-step explanation:

have a good day

To create a model of an artery, a health teacher uses the scale 2.5 cm : 0.75 mm. If the diameter of the artery is 2.7 mm, what is the diameter on the model?



a
9 m
b
90 cm
c
18 cm
d
9 cm

Answers

Answer: 9 cm

Step-by-step explanation:

I took the test

The rectangular floor of a classroom is 40 feet in length and 24 feet in width. A scale drawing of the floor has a length of 20 inches. What is the perimeter, in inches, of the floor in the scale drawing?

Answers

Answer:

Perimeter = 64 inches

Step-by-step explanation:

40':20" = 1':1/2"

24' =12"

20+20+12+12 = 64 inches

Evaluate expression: 3(5g + 5 - 2)

Answers

Answer: 15g + 9

Step-by-step explanation: Have a brilliant day!- Lily ^_^ Plz mark brainliest.

how do you solve 0.4m(40m-20n)

Answers

Answer:

= 16m2o−8mno

Step-by-step explanation:

make m the subject of the formula in 3-mx/2+2y=p/q​

Answers

It means we want to isolate m so...

mx/2+2y=p/q

mx/2=p/q-2y

mx=2p/q-4y

m=(2p/q-4y)/x

Hope this helped if you have any more questions ask it in questions.

Please do number 3___________________

Answers

9514 1404 393

Answer:

  m∠SVW = 80°

Step-by-step explanation:

3. The sum of same-side interior angles SVW (4x°) and VWT (5x°) is 180°. This can be used to solve for x and to find the angle values.

  4x + 5x = 180

  9x = 180 . . . . . . . . collect terms

  x = 20 . . . . . . . . . . divide by 9

m∠SVW = 4x° = 4(20)°

m∠SVW = 80°

_____

4. Then m∠VWT = 180° -80° = 100° = 5x°.

__

5. Consecutive interior angles are supplementary. ("Same-side" and "consecutive" are used interchangeably in this context.)

A one year member ship to your local gym costs $539. there is an initial fee of $35. write an equation tou can use to fund out how much you pay per month ​

Answers

$539 - $35 = $504

$504 : 12 = $42

Per month you pay $42.

I need help on this pleasee​

Answers

Answer:

slope is 6/0 which is undefined

Step-by-step explanation:

HELP ME PLSS!!

Oliver, Lily, and Ella are hoping to save money. Oliver thinks saving money in a shoe box in his closet every month is a good idea. He decides to start with $150, and then save $75 each month. Lily was given $4000 from her Great Uncle Merv, and decides to put the money into an account that has a 7% interest rate that is compounded annually. Ella has earned $4500 working at the gas station and decides to put her money in the bank in an account that has a 7.5% interest rate that is compounded continuously.

the question is Describe the type of equation that models Ella’s situation. Create that equation of Ella’s situation. Using the equation you created, how much money will be in Ella’s account after 2 years? 10 years?

Answers

You'd first have to divide the first to, then add an divide your sume by the percent to get your answer.

Answer:

Step-by-step explanation:

Use formulaic methods. Since she has interest on her money, we have to include it:

i = log(x-4*7)^k

i is the interested amount, x is the variable we use, and k is the number of times. 7 is the interest

i = log(4000-4x7)^2 for 4000 at 7% interest over 2 years

i = log(4000-4x7)^10 for 4000 at 7% interest over 10 years

Amount after 2 years: $30,000

Amount after 10 years: $15,671

Find a slope of each line (each block is one unit):

Answers

Answer:

The slope is -3

Step-by-step explanation:

We have two points

( -1,2) and (1,-4)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -4 -2)/ ( 1 - -1)

   = ( -4-2)/ (1+1)

   = -6/2

   = -3

Calculate the simple interest on $ 6400 at 10% p.a. for 9 months.​

Answers

this is the right answer good luck

3x(2ab - b) - 2y(2a - b)
please i need help!!​

Answers

Answer:

6abx-3bx-4ay+2by

Step-by-step explanation:

Answer:

The answer is 6xab - 3xb - 4ya + 2yb

Step-by-step explanation:

Factor the polynomial.

~Hoped this helped~

What is the reciprocal of 3 2/3

Answers

Answer:

the answer is 5

Step-by-step explanation:

Answer:

0.27272727272 is the reciproval of 3 2/3

If $18\sqrt 8-8\sqrt{18}=\sqrt n, what is n?

Answers

Answer:

288 trust me it is 100% right I tried it as an answer an got it right.

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

From the first two parts of the problem, we have

18√8 - 8√18 = 36√2 - 24√2

                    = (36 - 24)√2

                    = 12√2.

Thus, we wish to solve for n in the equation 12√2 = √n. In other words, we want to know what number 12√2 is the square root of. Any nonnegative number is the square root of its own square, so

n = (12√2)²

  = 12²(√2)²

  = 144 ∙ 2

  = 288.

Cand someone please help me with this assignment!!!

Answers

Answer:

1. 3

2. 4

3. 2

4. 1

5. 1

7. 3

8. 10?

thats all i know because thats my answers hope it helps

What is the area of the triangles? The problems are in the picture below. 15 points and a brainiest.

Answers

Answer:

first: 8 in^2

second: 77 yd^2

third: 225 in^2   (assuming that the larger triangle base =50 in (25 x 2)

Step-by-step explanation:

area = 1/2 x base x height

first:

1/2 x 4 x 4 = 8 in^2

second:

1/2 x 14 x 11 = 77 yd^2

third:

(1/2 x 50 x 18) - ( 1/2 x 18 x 25) = 450 - 225 = 225 in^2

Please help me, I am unsure how to do this

Answers

Answer:

-1/4

Step-by-step explanation:

Answer: -4 I think

Step by step: The equation for finding a slope is y2 -y1 /X2 - X1 and by x and y it means the coordinates so just pick a random two pair of coordinates and use that equation and if u chose (-1,4) and (1,-4) it will be -4-4/1- -1 which is -4. This works for any 2 coordinates. Sorry if that makes no sense lol

a deli made $320000 in revenue last year. Due to increased popularity of deli, the owner predicts that revenue will increase by 23% next year. How much revenue does the owner think the deli will generate next year?

Answers

This will be an educated guess but I think the answer would be $565000
Other Questions
Read the sentence from the passage.Hedgehog had curled up into a ball, while Tortoise had drawn his extremities, such ashis head, arms, and legs, into his shell.Which type of context clue is provided to help readers determine the meaning of extremities?O A. a definitionB. antonymsC. examplesD. cause and effectNeed help now please A: 5x+3xy +2y B: 2y-xy +4x: 12xy+4x-3y. then :- 1) -- , 2) 2A+3B+4C 3)3A-4B--2C. pls help me will mark u as brainliest which is the stronger acid?A pH 1B pH 4C pH 8D pH 13 how do the names of different Textiles tell us about their histories in a class of 48 student six upon one of the total number of students are girls how many students are girls in the class What is allocation by need please helppp Simplify.(-2)^-3 3x+9=36Show your steps what is nthe anwer 5 - 2x + 50 1. Lean los siguientes casos.cuaderno qu haran en cada situacin.En el saln de Isabelhan desaparecido algunas cosas.Nadie haba visto nada... hasta ayer,cuando Isabel entr al saln y viocuando Claudia meta el chaleco deuna de sus compaeras ensu mochila. Isabel no sabe si debecontarle a la maestra, puesClaudia ha sido su amiga desdeque eran pequeas.En la Feria d help please13 points!!! What is the area of the real bedroom? Humans should consider microbes as beneficial organisms for all of the following reasons except:Group of answer choicesthey purify water in the hydrosphere.they consume carbon dioxide during photosynthesis.they decompose organic waste in the geosphere.they generate oxygen in the hydrosphere.they filter ultraviolet radiation in the atmosphere. 2/7 of the person at a concert are children 1/4 and men and the rest women what fraction are women Escribe cul es la importancia de la escenografa en una obra teatral A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 . When 2 dice are rolled, the sum of both faces is calculated. Determine theprobability of the event: Rolling a sum of 10. Justify your answer. a torque of 24 ft pounds is the result when a force of ______ pounds is applied to a wrench that is 18 inches long. Why might Robert choose to attend a technical school rather than a four-year university?Select one:a. There are more options and greater earning potential at technical schools.b. There are more opportunities for advancement in technical schools.c. Some trades are in higher demand than certain university degrees.d. The social aspect of technical schools is more appealing. q + 4 = 19 solve for q