I came across a problem that asked whether $\displaystyle \sum_{n=1}^\infty \sin(\pi\sqrt{n^2+1}) $ converges or not. I was able to show that it converges (ask if you'd like to see why), but I was wanting to take this a step further:

What does $\displaystyle \sum_{n=1}^\infty \sin(\pi\sqrt{n^2+1}) $ converge to? I'm under the impression that there might not be an answer expressible in terms of finite composition of elementary functions but I'm not sure.

Thanks everybody

-Chip