Use the Integral Test to determine the convergence or divergence of the series

1. 1/2 + 1/5 + 1/10 + 1/17 + 1/26

Are you supposed to find a formula and then integrate that?

I'm assuming that goes on forever, rather than just stopping at 1/26.

Probably...it's 1/(n^2 + 1). That integrates to arctan x, from 1 to infinity (or from 1 to b as b approaches infinity), which is pi/2 - arctan(1). It converges.

Yes you are supposed to find a formula first, which is t(n) = 1/(n^2 + 1)

This series converges if and only if the integral from 0 to infinity is finite, which it is. It's π/2.

Yes, you are.

In this case, the formula seems to be
a(n) = 1/(n^2 + 1)

Integrate that and find that the integral is finite --> convergence