Sum of a Series from Partial Sums

Question

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 $$\displaystyle \sum_{k=1}^{\infty} a_k$$?

Accepted Answer

$$\displaystyle 	ext{The series diverges.}$$

Answer

$$\displaystyle 0$$

Answer

$$\displaystyle \frac{1}{2}$$

Answer

$$\displaystyle -1$$

Sum of a Series from Partial Sums

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