 My Math Forum Mathematical Induction technicality help wanted!

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 February 5th, 2012, 08:21 PM #1 Newbie   Joined: Oct 2011 Posts: 22 Thanks: 0 Mathematical Induction technicality help wanted! Hey anyone can help me with a little confusion here: Prove that 0+1+...+n = n(n+1)/2 I did the base case, where P(0) is 0 on the left and right hand sides. I made the inductive hypothesis: ...+k= k(k+1)/2 Then to show P(k+1) is also true: 0+1+...+k +(k+1) = k+1((k+1)+1)/2 Using the i.h. we plug into this and get: k(k+1)/2 + (k+1) = k+1(k+2)/2 I left the right hand side alone since that's the desired result we need on the left hand side. However the left hand side I got lost. I tried distributing: k^2+k/2 + k+1 but that doesn't equal the right hand side! Unless I'm overlooking things, or just need to see a different algebraic manipulation here. Thanks in advance to those who help me!  February 5th, 2012, 08:31 PM #2 Global Moderator   Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5 Re: Mathematical Induction technicality help wanted! (k^2 + k)/2 + k + 1 = (k^2 + k)/2 + 2(k + 1)/2 = [k^2 + k + 2k + 2]/2 = ... The right hand side. You need a common denominator of 2 on the LHS in order to combine into one fraction. Tags induction, mathematical, technicality, wanted ### mathematical technicality

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