Find the least positive integer $N$ for which $\sum_{r=N+1}^{\infty}\frac1{r(r+1)}

Question

Find the least positive integer $N$ for which $\sum_{r=N+1}^{\infty}\frac1{r(r+1)}<0.01$.

Accepted Answer

$N=100$, because the tail equals $1/(N+1)$.

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