Question

Prove the alternating series test by showing that (sn) is a cauchy sequence.

Answer 1

Answer: Given an > 0 we need an N such that n, m > N means |sn â’ sm| < . We are free to assume that n > m (since they otherwise play symmetric roles in the definition of a Cauchy sequence). Then sn â’ sm = (â’1)mam+1 + . . . + (â’1)nâ’1 an = (â’1)m