∑∞n=1−4(−1/2)n−1
∑∞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.
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