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Math Help - Deduce the inequality

  1. #1
    Junior Member
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    Deduce the inequality

    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

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

    Is true by induction, but I am then asked to deduce that

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

    Can someone please point me in the right direction.

    Thanks
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  2. #2
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    Quote Originally Posted by bobred View Post
    I have shown that
    \sum_{r=1}^{n}\frac{r}{2^r}=2-\frac{n+2}{2^n} for n=1,2,3,...
    Is true by induction, but I am then asked to deduce that

    \sum_{r=1}^{n}\frac{r}{2^r}<2 for n=1,2,3,...
    2-\frac{n+2}{2^n} <2 because -\frac{n+2}{2^n} <0
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