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Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 67

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

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

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

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

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...

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

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

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

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