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I would like to prove this by induction. How can I approach this, or maybe give me an answer and show me how you did this in detail? I'm struggling with using induction and would like to expand my knowledge. Would really appreciate your help, Thanks

Roy Kesserwani
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  • http://math.stackexchange.com/questions/87030/proving-sum-limits-i-0n-i-2i-1-n1-2n-1-by-induction – lab bhattacharjee Apr 07 '14 at 19:01
  • What have you attempted? What is causing confusion? This is your second post in under an hour involving very similar induction problems. In both posts you've provided an image of the problem from what appears to be the same assignment/textbook and left the same message about how you're confused/struggling. What you haven't done is provided any indication of what you're confused by or struggling with. You'll learn a lot more by posting your attempted solutions as part of your questions (along with any road blocks you encounter) and allowing us to recommend how to proceed. – Dan Apr 07 '14 at 19:35

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Assuming $$\sum_{i=1}^{n}{n2^n}=(n-1)2^{n+1}+2$$ we get $$\sum_{i=1}^{n+1}{n2^n}=(n-1)2^{n+1}+2+(n+1)2^{n+1}=2^{n+1}\left((n-1)+(n+1)\right)+2=2^{n+1}(2n)+2=n2^{n+2}+2$$

user140943
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