I'm trying to show that, given a sequence of random variables $\{T\_n\}\_{n\in\mathbb{N}}$, we have:
$$
\lim\_{n\to\infty}\mathbb{E}\left[|T\_n-c|^2\right]=0\iff
\lim\_n\mathbb{E}(T\_n)=c, \lim\_n V(T\_n)=0
$$
I managed to show $(\Leftarrow)$, but I'm stuck on $(\Rightarrow)$. Can anyone give me some *hints*?

Thanks for helping!