Does the series converge or diverge? If it converges, what is the sum? Show your work.

Question

(∑∞n=1) −4(−1/2)n−1

Answer 1

We can rewrite the series as:

(-4) ∑∞n=1 (-1/2)n-1

Note that the sum inside the parentheses is a geometric series with first term 1 and common ratio -1/2, so we can use the formula for the sum of a geometric series:

∑∞n=1 (-1/2)n-1 = 1/(1-(-1/2)) = 2

Therefore, the original series converges and its sum is:

(-4)(2) = -8