# 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 $\sum_{k=1}^{\infty} k r^k$.