# Telescoping Series Proofs

Prove telescoping series:

Let a_n from n=0 to infinity be a sequence of real numbers which converge to 0, i.e. lim n-->infinity a_n=0. Then the series of the sum from n=0 to infinity of (a_n - a_n+1) converges to a_0.

Hint: first work out what the partial sums of the sum from n=0 to N of (a_n - a_n+1) should be, and prove your assertion using induction.

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#### Solution Summary

The expert proves telescoping series.

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