Math for Non-Geeks/ Exercises: Convergence criteria for series

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Root and ratio test: estimate of errors

In some cases, the infinite sum $s=\sum _{k=1}^{\mathrm{\infty }}{a}_k$ 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 $|s-s_n|$:

Further convergence criteria

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