What is an oscillating infinite series?

Answer 1

I believe that it is the same as an alternating series. If that is the case, then an oscillating series is a series of the form:

#sum_{n=0}^infty (-1)^n b_n#, where #b_n ge 0#.

For example, the alternating harmonic series

#sum_{n=1}^infty{(-1)^n}/n#

is a convergent alternating series.

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Answer 2

Scarlett Allison

An oscillating infinite series is a series whose terms alternate in sign as the series progresses. In other words, the terms of the series switch between positive and negative values. This alternation creates a pattern of oscillation or fluctuation in the sum of the series as more terms are added. These series often do not converge to a single finite value but rather oscillate indefinitely or converge conditionally to a specific limit. Examples of oscillating infinite series include the alternating harmonic series and some trigonometric series.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.