Consider the following infinite series:
(a) \(\displaystyle \sum_{n=1}^{\infty} \frac{\sin (n \pi / 2)}{\sqrt{n}}\), (b) \(\displaystyle \sum_{n=1}^{\infty} \log \left(1+\frac{1}{n^2}\right).\)
Which one of the following statements is true?
1
(a) is convergent, but (b) is not convergent.
2
(a) is not convergent, but (b) is convergent.
3
Both (a) and (b) are convergent.
4
Neither (a) nor (b) is convergent.