Telescoping Series Test

Equation
$$\sum_{n = 0}^{oo} \frac{1}{f(x) * g(x)}$$

Use
First, if the equation shown above is in the form of a trinomial, find the partial sums of the summation.A telescoping series will have many cancellations through its summation.Add up all of the non canceled terms, this will often be the first and last terms.Subtract the last term of the limit to from the first to find the series convergence

Explanation
In a alternating series every term will have a sign different than the term before it. This will cause many terms to cancel each other out. Since the terms are continuously getting smaller, and cancelling out, the series will converge.

Video Explanation


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