SOLUTION: Does the series converge or diverge? If it converges, what is thr sum? E -4(-1/2)^n-1 n=1

SOLUTION: Does the series converge or diverge? If it converges, what is thr sum? E -4(-1/2)^n-1 n=1

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Question 1117531: Does the series converge or diverge? If it converges, what is thr sum?
E -4(-1/2)^n-1
n=1
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Step 1: Plain text notation lesson. sum[1,infty] -4(-1/2)^(n-1) would be interpreted as

2. Convergence: A geometric series converges if the common ratio

is in the interval

. Since

, this series converges.

The sum of a convergent geometric series of the form

is given by

The rest is just arithmetic.

John

My calculator said it, I believe it, that settles it

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