APFIVE Sum of a Series from Partial Sums
The infinite series $$\displaystyle \sum_{k=1}^{\infty} a_k$$ has nth partial sum $$\displaystyle S_n = (-1)^{n+1}$$ for $$\displaystyle n \geq 1$$. What is the sum of the series $$\displaystyle \sum_{k=1}^{\infty} a_k$$?
A
$$\displaystyle -1$$
B
$$\displaystyle 0$$
C
$$\displaystyle \text{The series diverges.}$$
D
$$\displaystyle \frac{1}{2}$$
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