# Infinite series with all negative terms

1. Nov 14, 2015

### Ibraheem

Hello,

I have been reviewing my textbook lately, and I came across a rather paradoxical statements. all of the convergence tests in my book state that the terms of the series has to be positive. However, when I solved this power series ∑(-1)n-1(xn/n), I found that it converges for -1<x≤1, but when I plugged -0.45 to test if the infinite series will converge, I got all the terms negative. So my question is can a series converge if all its terms are negative?

2. Nov 14, 2015

### Staff: Mentor

Yes. E.g. $-e$.