8.9k views
3 votes
Find 10 partial sums of the series. (round your answers to five decimal places.) ∞ 15 (−4)n n = 1

2 Answers

4 votes

Find 10 partial sums of the series. (Round your answers to five decimal places.)

15 /(−4)n

Do calculations based on answer above (i.e. 15/(-4)^1 + 15/(-4)^2+...

1

-3.75000

Correct: Your answer is correct.

2

-2.81250

Correct: Your answer is correct.

3

-3.04688

Correct: Your answer is correct.

4

-2.98828

Correct: Your answer is correct.

5

-3.00293

Correct: Your answer is correct.

6

-2.99927

Correct: Your answer is correct.

7

-3.00018

Correct: Your answer is correct.

8

-2.99995

Correct: Your answer is correct.

9

-3.00001

Correct: Your answer is correct.

10

-3.00000

Correct: Your answer is correct.

Graph both the sequence of terms and the sequence of partial sums on the same screen.

WebAssign Plot WebAssign Plot

WebAssign Plot WebAssign Plot

Correct: Your answer is correct. (The one converging near -3, black dots)

Is the series convergent or divergent?

convergent

Correct: Your answer is correct.

If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.)

set up calculations to determine convergence (geometric)

a/1-r

a=15/-4 , r=1/-4

-3

Correct: Your answer is correct.

User Dimitar Christoff
by
8.3k points
5 votes
Given


\Sigma_(n=1)^\infty15(-4)^n

The first 10 partial sums are as follows:


S_1=\Sigma_(n=1)^(1)15(-4)^n=15(-4)=\bold{-60} \\ \\ S_2=\Sigma_(n=1)^(2)15(-4)^n=\Sigma_(n=1)^(1)15(-4)^n+15(-4)^2 \\ =-60+15(16)=-60+240=\bold{180} \\ \\ S_3=\Sigma_(n=1)^(3)15(-4)^n=\Sigma_(n=1)^(2)15(-4)^n+15(-4)^3 \\ =180+15(-64)=180-960=\bold{-780} \\ \\ S_4=\Sigma_(n=1)^(4)15(-4)^n=\Sigma_(n=1)^(3)15(-4)^n+15(-4)^4 \\ =-780+15(256)=-780+3,840=\bold{3,060} \\ \\ S_5=\Sigma_(n=1)^(5)15(-4)^n=\Sigma_(n=1)^(4)15(-4)^n+15(-4)^5 \\ =3,060+15(-1,024)=3,060-15,360=\bold{-12,300}


S_6=\Sigma_(n=1)^(6)15(-4)^n=\Sigma_(n=1)^(5)15(-4)^n+15(-4)^6 \\ =-12,300+15(4,096)=-12,300+61,440=\bold{49,140}

The rest of the partial sums can be obtained in similar way.
User Harun ERGUL
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories