I ran across these two problems, while reading a text on number theory. The problem states: "Verify the following identities". What does "verify" mean in this context, and what strategies can I employ in trying to solve these questions?
1.) $\zeta(s)^{-1}= \sum^{\infty}_{n=1}\mu(n)/n^{s}$
2.) $\zeta(s)^{2}= \sum^{\infty}_{n=1}\nu(n)/n^{s}$
where $\zeta(s)=\sum^{\infty}_{n=1}1/n^{s}$ is the Riemann $\zeta$ function, $\mu(n)$ is the Möbius $\mu$ function and $\nu(n)$ counts the number of positive divisors of n.