So far my problem is finding E(X). After all my attempts I have E(X) = a/(a+1), and even wolfram alpha backs me up on this, even though the answer my prof got was a/(a-1). Sorry it's a picture again, but my rough work
I believe my set up and integration was right, but somewhere in evaluating the limit I went wrong. It's such a simple mistake but it's so irritating.
Your mistake is as you integrate
$$\int_1^\infty x^{-\alpha} \, dx = \left.\frac{x^{-\alpha+1}}{\color{red}-\alpha+1}\right|_1^\infty$$