Convergence of Power Series at different value

Question

I know C is the correct answer using the Ratio Test. (Wrong)

But why the series might not converge when x = 2?

I tried using the Direct Comparison Test and it seems that $a_n2^n > a_n(-1)^n$ and the series with x = 2 should converge as well since the larger series converges.

Answer 1

This question doesn't make any sense as C isn't even true if $$a_n=\frac{(-1)^n}{(n+1)2^n}$$