Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with simple proof by mathematical induction

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    0^2 + 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6

    2. Relevant equations

    3. The attempt at a solution

    I'm confused on how to prove this by induction. I'm not exactly sure what the goal of the rearrangement is after substituting (n+1). Any help is much appreciated!

    base case: n = 0
    0^2 = 0(0+1)(2*0+1)/6

    induction step:
    (0^2+1^2+2^2+...+n^2) + (n+1)^2 = (n+1)((n+1)+1)(2(n+1)+1)/6

    n(n+1)(2n+1)/6 + (n+1)^2

    (n+1)[n(2n+1)/6 + (n+1)]
    ...here is where I'm lost, I'm not sure what I'm trying to manipulate it to look like....

  2. jcsd
  3. May 2, 2010 #2


    User Avatar
    Homework Helper

    Factor out 1/6 and then simplify what is left in the brackets.
  4. May 2, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You're trying to show the first equation is true. To do this, you start with one side, as you have done, and manipulate it until it looks like the other side.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook