Another convergence problem

[mooshupork34]

I was confused as to how to do this, so any help would be appreciated:

I have to see if the following series converges and justify my answer.$\sum_{j=1}^{\infty}(-1)^{j}(1-\frac{1}{j})$

 

[soroban]

Hello, mooshupork34!

Test for convergence: \(\displaystyle \L\:\sum_{j=1}^{\infty}(-1)^{j}(1-\frac{1}{j})\)

The general term: \(\displaystyle \L\:a_n\:=\-1)^n\left(1\,-\,\frac{1}{n}\right)\) does not approach zero.

. . The series diverges.

 

[mooshupork34]

Thanks! Question, though. Why doesn't it approach zero?

 

[stapel]

Why doesn't it approach zero?

What does 1/n approach? So what does 1 - (1/n) approach?

Eliz.