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**Sneaky** Wn has density [1+(x/n)]/[1+(0.5n)] for 0<x<1, and 0 otherwise. The random variable W has a uniform distribution on [0,1]. Prove that {Wn} converges in distribution to W.

I have so far that

mWn(s)=E(e^(sWn))= integral (0 to 1): e^(sWn)*((1+(x/n)))/(1+(1/2n))dWn

= ((1+(x/n)))/(1+(1/2n)) * integral (0 to 1): e^(sWn)dWn

which equals (as lim n-> inf.)

integral (0 to 1): e^(Sw)dw

mW(s)=E(e^(Sw))=integral (0 to 1): e^(Sw)dw

But now how do I show the convergence?

Any help is appriciated.