Investigate the Alternating Series $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^{2}}$
A) the P- Series $\sum_{n=1}^{\infty} \frac{1}{n^{2}}$

Multiple Choice

Investigate the alternating series $\sum_{n=1}^{\infty} \frac{(-1) ^{n+1}}{n^{2}}$ .

A) The p- series $\sum_{n=1}^{\infty} \frac{1}{n^{2}}$ converges, so the series $\sum_{n=1}^{\infty} \frac{(-1) ^{n+1}}{n^{2}}$ converges absolutely.
B) The p-series $\sum_{n=1}^{\infty} \frac{1}{n^{2}}$ diverges, so the series $\sum_{n=1}^{\infty} \frac{(-1) ^{n+1}}{n^{2}}$ converges conditionally.
C) The ratio test gives $\mathrm{r}=1$ , so the series $\sum_{\mathrm{n}=1}^{\infty} \frac{(-1) ^{\mathrm{n}+1}}{\mathrm{n}^{2}}$ diverges.
D) The p-series $\sum_{n=1}^{\infty} \frac{1}{n^{2}}$ diverges, so the series $\sum_{n=1}^{\infty} \frac{(-1) ^{n+1}}{n^{2}}$ diverges.