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Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 67

The article gives specific rearrangements of the alternating harmonic series.

The author argues that many topics in differential and integral calculus could be better approached by an appropriate use of geometric series.

The author uses differentiation to obtain a standard formula for sums of the form \(1^k + 2^k + \ldots + n^k\), where \(n\) and \(k\) are positive integers.

For series with non-zero terms, the Root Test is interpreted in terms of the geometric mean of the ratios of successive terms (in absolute value). The author also consders the test obtained by...

The author describes an application of the telescoping series, \( \sum_{k=1}^{\infty}  \frac{1}{k(k+1)}\), to the visual theory of perspective.

The author gives an elementary proof of the convergence of p-series for p > 1.

Bounds are obtained for the sums of powers of the first \(n\) integers.

It is shown that there are conditions in which comparison tests apply to series with negative terms.

The author summarizes a variety of ways to approximate \(\pi\).

Visual proof of a geometric series identity

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