Exercises: Convergence criteria for series – "Math for Non-Geeks"

Root and ratio test: estimate of errors

In some cases, the infinite sum $s=\sum _{k=1}^{\infty }a_{k}$ cannot be computed explicitly. We can try to approximate it by $s_{n}=\sum _{k=1}^{n}a_{k}$. The following exercises are devoted to giving upper bounds on the approximation error $|s-s_{n}|$: