The Weierstrass $M$-test says that if $(f\_n$) is a sequence of functions on $E$, and $\left|f\_n(x)\right|\leq M\_n$, then $\sum f\_n$ converges uniformly on $E$ if $\sum M\_n$ converges. 

My question is, can $M\_n$ depend on $x$? that is, if I know $\left|f\_n(x)\right|\leq \dfrac{1}{x^2n^2}$ (whose sum does converge), is this sufficient?