Question

Does the series 4/5 - 2/5 + 1/5 -1/10+... converge or diverge? If it converges what is the sum.

Answer 1

Well, the rule for the terms seems to be \(\large a_n=-\frac{8}{5}(-\frac{1}{2})^{n}\). So it converges, because it is alternating and each term is less than the last term and the terms approach zero.

It is actually a simple geometric series, \(\large \sum\limits_{n=1}^{\infty}(-\frac{8}{5})\left (-\frac{1}{2}\right )^n\), so the sum follows from that formula, it is 8/15.