Hi

If this is the wrong section of the forum to post this I apologise, if so could you tell me which one would be more appropriate?

The answer is probably staring me in the face, but here goes.

I have shown that

$\displaystyle \sum_{r=1}^{n}\frac{r}{2^r}=2-\frac{n+2}{2^n} $ for $\displaystyle n=1,2,3,...$

Is true by induction, but I am then asked todeduce that

$\displaystyle \sum_{r=1}^{n}\frac{r}{2^r}<2$ for $\displaystyle n=1,2,3,...$

Can someone please point me in the right direction.

Thanks