Question 144
For each positive integer $n$, let $\varphi(n)$ be the number of positive integers from $1$ to $n$ that are relatively prime to $n$. Evaluate
$$
\sum_{n=1}^{\infty} \frac{\varphi(n) 4^{n}}{7^{n}-4^{n}}
$$
$$
\sum_{n=1}^{\infty} \frac{\varphi(n) 4^{n}}{7^{n}-4^{n}}
$$