# What is a collapsing infinite series?

Here is an example of a collapsing (telescoping) series

by cancelling ("collapsing") the overlapping terms,

Hence, the sume of the infinite series can be found by

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A collapsing infinite series is a type of infinite series where most terms cancel each other out, leaving only a finite number of non-zero terms. As more terms are added, the partial sums of the series converge to a finite value. This convergence occurs because the remaining non-zero terms eventually become insignificant compared to the overall behavior of the series. The term "collapsing" refers to the reduction or cancellation of terms during the process of summation, resulting in a simplified and convergent series.

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