To determine if the series converges or diverges, we can use the formula for a geometric series:
∑∞n=1ar^n= a / (1 - r)
where a is the first term and r is the common ratio. In this case, a = -4 and r = -1/2.
Plugging in these values, we get:
∑∞n=1-4(-1/2)^n-1 = -4 / (1 + 1/2) = -4 / (3/2) = -8/3
Therefore, the series converges and the sum is -8/3.
Does the series converge or diverge? If it converges, what is the sum? Show your work.
∑∞n=1−4(−1/2)n−1
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