Question

Does this sequence converge or diverge? a(n)= (n+(-1)^n)/n, and find the limit if it is convergent.

Answer 1

limit is 1 yes

Answer 2

Well, you can write \[\sum_{n=1}^{\infty} (n+ (-1)^n)/n = \sum_{n=1}^{\infty} (1+ (-1)^n)/n) = \sum_{n=1}^{\infty}1 + \sum_{n=1}^{\infty}(-1)^n)/n)= \infty\] because you add up an infinite sequence of 1ones. Hope this is right...