Spring 2017, problem 39
Let $a_{n+1} = a_n + \frac{1}{{a_n}^{2017}}$ and $a_1=1$. Show that the sum $\sum^{\infty}_{n=1}{\frac{1}{n a_n}}$ converges.
Let $a_{n+1} = a_n + \frac{1}{{a_n}^{2017}}$ and $a_1=1$. Show that the sum $\sum^{\infty}_{n=1}{\frac{1}{n a_n}}$ converges.