Monday
November 24, 2014

Homework Help: Pre-cal

Posted by Lucy on Saturday, January 3, 2009 at 11:46am.

use mathematical induction to prove that 1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6 for all positive integral values of n.

My work: n=1: 1(1+1)(2(1)+1)/6 = 1(2)(3)/6 = 6/6 = 1.

1^2+2^2+3^2...(n-1)^2+n^2= [(n-1)(n-1)+2n(n-1)+1]/6 = 2n^3+3n^2+n/6 = n(2n=1)(n+1)/6 = n(n+1)(2n+1)/6. Since Sn is valid for n=1, it is also valid for n=2, n=3, etc.

The teacher marked this as wrong but this followed the example provided by the book. Where did I go wrong?

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