1. ## alternating series test

Hi all,

I was wondering for the following series:

$
\sum_{n=1}^{\infty}\frac{(-1)^(n-1)(-1)^n}{n}
$

NOTE: in the numerator it is meant to be (-1)^(n-1) times by (-1)^n .... sorry i can't it get the code to work

are you allowed to let a_n = (-1)^n/ n and say that since a_n is not >0 for all n>=1, therefore the series diverges?

ArTiCk

2. Originally Posted by ArTiCK
Hi all,

I was wondering for the following series:

$
\sum_{n=1}^{\infty}\frac{(-1)^{n-1}(-1)^n}{n}
$

NOTE: in the numerator it is meant to be (-1)^(n-1) times by (-1)^n .... sorry i can't it get the code to work

are you allowed to let a_n = (-1)^n/ n and say that since a_n is not >0 for all n>=1, therefore the series diverges?

your $a_n = \frac 1n$ here. so, $\lim_{n \to \infty}a_n = 0$
Note that $(-1)^{n - 1}(-1)^n = (-1)^{2n - 1} = -1$, thus your series is $\sum_{n = 1}^\infty \frac {-1}n$, which is a divergent harmonic series. The alternating series test does not apply since you do not have an alternating series.