To determine if the series converges, we can rewrite it as:
∑^∞ n=1 -4(-1/2)^(n-1)
This is a geometric series with a common ratio of -1/2 and first term of -4.
The sum of an infinite geometric series is given by:
Sum = a / (1 - r)
where a is the first term and r is the common ratio.
Plugging in the values into the formula:
Sum = -4 / (1 - (-1/2))
Sum = -4 / (3/2)
Sum = -4 * (2/3)
Sum = -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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