Question

how do i get divergent with series (-1)^n from 0 to infinity??

Answer 1

Geometric series test!
\[\sum_k r^k~\text{ diverges for }|r|\ge1\]

Answer 2

thanks!

Answer 3

you're welcome!

Answer 4

Observe \((-1)^n\) yields the partial sums \(1,0,1,0,\dots\) and clearly these do not converge :-p

Answer 5

true true..... is that a good method to use sometimes in finding convergence or divergence when it comes to series?

Answer 6

Which one, the partial sums check or the geometric series test?

If I'm not mistaken, the first always works (though can be quite difficult). The second only applies for geometric series.

Answer 7

yeah the partial sums check...thank you both!