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.© BrainMass Inc. brainmass.com October 10, 2019, 4:39 am ad1c9bdddf
The expert proves telescoping series.