Originally Posted by

**inthequestofproofs** Hello

I am trying to figure out if the following sequence converges:

Pn={(1/n)*sin(npi/2))} from n=1 to infinity.

This is how I am approaching it. I am using the fact that a sequence converges iff all of its subsequences converge to the same limit. So, I assume that Pn converges to p.

Then, I look at the subsequence {sin(npi/2)}. This subsequence doesn't converge because it fluctuates between -1,0 and 1 depending on the value of n. So, since this sequence doesn't have a limit and it doesn't converge, then Pn diverges. Am I right?

Thanks