Solution (source code)

= Solution

The <comparison test for series> states that if $0\leq u_n\leq v_n$ for all sufficiently large $n$, convergence of $\sum v_n$ implies convergence of $\sum u_n$. Equivalently, divergence of the smaller nonnegative series forces divergence of the larger one. Finitely many initial terms do not affect either convergence conclusion.