Infinite Series: Convergence and Absolute Convergence

[fjotlandj]

Given that the series from n = 1 to infinity of An converges to L, which of the following conclusions is valid for the series from n = 1 to infinity of (An)^2?

A) It may diverge
B) It converges absolutely
C) It converges to M < L
D) It converges to M > L
E) It converges to M^2 = L

My intuition tells me the answer is E). But I am not sure can someone help figure this out please

 

[rs1n]

Given that the series from n = 1 to infinity of An converges to L, which of the following conclusions is valid for the series from n = 1 to infinity of (An)^2?

A) It may diverge
B) It converges absolutely
C) It converges to M < L
D) It converges to M > L
E) It converges to M^2 = L

My intuition tells me the answer is E). But I am not sure can someone help figure this out please

Hints: convergent geometric series (this should eliminate some of the possible answers). Then look up what it means to converge absolutely, and play around with

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