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Thread: Summation prove by induction

  1. #1 Summation prove by induction 
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    Hey guys,

    I am working on the following proof but I am very very stuck....
    ANy input is greatly appreciated...


    Prove by induction that for each integer n > 1,
    Summation from i=1 to n of (i*2^i)= 2+(n-1)*2^(n+1)


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  3. #2  
    Forum Professor serpicojr's Avatar
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    Well, what do you have so far?


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  4. #3  
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    I get down to the induction step but I dont know what to do with it.

    After the base step is verified, assume 2+(k-1)*2^(k+1) is true to prove that 2+(k+1-1)*2^(k+1+1) = 2+k*2^(k+2).

    This is where my proof stops...dont know how to go forward...
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  5. #4  
    Forum Professor serpicojr's Avatar
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    So what's the difference for the sum for k and for the sum for k+1?
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