Consider a real valued function $\displaystyle f(x)$ satisfying, $\displaystyle 2f(xy) = (f(x))^y + (f(y))^x$ for all real $\displaystyle x\ \mbox{\&}\ y$ and $\displaystyle f(1) = a$ where $\displaystyle a\neq 1$. Prove that $\displaystyle (a - 1)\sum_{i = 1}^{n}f(i) = a^{n + 1} - a$.