Does absolute convergence imply the convergence of square of the sequence?

Question

I know the 1st option isn't necessarily true ,since $\{(-1)^n\}$ is not convergent,but it's absolute convergent. But I am stuck between the 2nd and 3rd option.

Answer 1

Well using your own example $$S_n=(-1)^n$$ you can prove that A, C, D are false so B needs to be the true one. C would produce a sequence of 0,2,0,2..., while D would produce 0,-2,0,...

Answer 2

Since $f(t)=t^2$ is continuous, $|s_n|\to s$ implies $s_n^2 \to s^2$.