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.Im attaching the proof in .docx and .pdf formats.




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