Question

Determine whether the following series converges or diverges.

(-1)^(n-1)/sqrt(n)

Answer 1

alternating, so as long as the terms go to zero it converges

Answer 2

i believe this converges because of the alternating series but i wanted to ask what do you have to look at to know if it converges when there is a square root in the denominator?

Answer 3

by "series" i assume you mean
\[\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{\sqrt{k}}\]

Answer 4

converges because
a) it is alternating and
b)
\[\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}=0\]

Answer 5

yes that is what i mean

Answer 6

ohh so as the nth term gets bigger in the denominator the limit gets closer and closer to zero, correct?