Let $\sum_{n=1}a_n,\ a_n>0$ be a convergent series. Consider following statements:
- P: The series $\sum_{n=1}\sqrt{a_n}$ is always convergent
- Q: The series $\sum_{n=1} \frac{a_1 + a_2 +...+a_n}{n}$ is always divergent
Then
- Both P and Q are true,
- P is true but Q is false,
- Both P and Q are false,
- P is false and Q is true
I was thinking of suitable examples/counterexamples but I could not find any. Please suggest.
Thanks