## Problem of the week

### 2019-05 Convergence with primes

Let $$p_n$$ be the $$n$$-th prime number, $$p_1 = 2, p_2 = 3, p_3 = 5, \dots$$. Prove that the following series converges: $\sum_{n=1}^{\infty} \frac{1}{p_n} \prod_{k=1}^n \frac{p_k -1}{p_k}.$