Does the series converge or diverge? If it converges, what is the sum? Σ∞ n=1 -4(-1/3)^n-1

Answer 1

The given series is a geometric series with first term a = -4 and common ratio r = -1/3.

To determine if the series converges, we can use the formula for the sum of an infinite geometric series, which is S = a / (1 - r).

Plugging in the values for a = -4 and r = -1/3, we get:

S = -4 / (1 + 1/3) = -4 / (4/3) = -3

Therefore, the series converges and the sum is -3.