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Browse Classroom Capsules and Notes

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Displaying 41 - 50 of 67

The author gives a proof of Stirling's formula accessible to the first year calculus students.

The subseries of the harmonic series, \(\sum_{n=1}^{\infty} \frac{1}{n}\), which consists of all terms with one or more nines in the digits of \(n\), is a divergent series.

Clever partitioning of a square into three equal regions yields an alternating series summing to 1/3.

Using integration, the author finds the sums of a class of series whose denominators involve bionomial coefficients.

The sum of reciprocals of triangular numbers is computed visually.

The author provides a concise proof that \(\sum_{n=0}^{\infty}1/(2n+1)^2 ={\pi}^2/8\).

The authors provide several examples of evaluating difficult limits by using Riemann sums. Note that many of these limits are usually solved by Stirling's formula or series methods....

This is a short proof of a famous result of Euler about summation of the following series: \(\sum 1/{n^2} = {\pi^2}/6\).

A variation of a well-known approximation of \(e\) is analyzed.

The author presents an easy absolute convergence test for series based solely on differentiation, with examples.

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