Determine whether the following series converges or diverges.

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

Question

Determine whether the following series converges or diverges.

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

anonymous · Answer

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

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yes that is what i mean

anonymous · Answer

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