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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §10.2 Convergence Tests: Positive Series, #29 · Calculus · Series

… is “telescoping” because … and … cancel … and

$(\frac{1}{1} - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4})$ is “telescoping” because $\frac{1}{2}$ and $\frac{1}{3}$ cancel $- \frac{1}{2}$ and $- \frac{1}{3}$ . Add the infinite telescoping series
$s = 1 \sum \infty (\frac{1}{n} - \frac{1}{n + 1}) = 1 \sum \infty (\frac{1}{n ( n + 1 )}) .$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §10.2 Convergence Tests: Positive Series, #29

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