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Browse Classroom Capsules and Notes

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A geometric proof of the sum of an infinite series. Gabriel's Staircase is \(\sum_{k=1}^{\infty} k r^k\).
A geometric proof of the sum of geometric series

A geometric construction of a monotone sequence bounded above by \(e\).

A visual solution for an alternating sum of odd squares is presented.

The author provides a visual solution for the alternating sum of an even number of triangular numbers.

Hansheng Yang and Heng Yang used the arithmetic-geometric mean inequality to prove that the sequence \([1+1/n]^n\) is monotonic increasing converging to \(e\) whereas \([1+1/n]^{n+1}\) is...

Infinite series representing several functions, and several series representing \(\pi\) are derived using tabular integration by parts.

In this note the convergence of certain modified \(p\) -series is discussed.

A new way to derive infinite series expressions for \(\ln 2\) and \(\ln 3\)

The author generalizes the test of convergence for the series involving iterated logarithms from base \(e\) to any positive base.