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Browse Classroom Capsules and Notes

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This capsule investigates the sequences that converge to Euler's constant. By utilizing the geometric description of the terms, the author can obtain a rate of convergence comparable to...

Certain p-series are the focus of this capsule. This project comes with scenarios to help students "visualize" the convergence or divergence of the p-series.

The result is illustrated for ratio 1/9, via an approach that is readily generalized.  In particular, the result \( \frac{1}{n} + \frac{1}{n^2}  + \frac{1}{n^3} + \cdots = \frac{1}{n...

In this note an elementary proof of Stirling's asymptotic formula for \(n!\) is given.

The result in the title is demonstrated graphically.

Mengoli`s Series is presented visually .

Two proofs, one elementary, of the limit in the title are presented.

The limit of the ratio of the geometric mean to the arithmetic mean of certain sequences is studied, using Riemann sums.

The authors show that a certain sequence unexpectedly converges to 8.

The author uses the Stolz-Cesàro theorem to compute the sums of the integer powers.