# Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

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.