Mathematical Induction

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March 21st 2011, 04:32 PM
compstudent

Mathematical Induction

I am having problems solving the second step. I have proven that n=1 in the first step.

I have to prove each given statement through mathematical induction.

http://i53.tinypic.com/34phphc.gif

Help would be greatly appreciated (Nod) Thank you
March 21st 2011, 04:52 PM
pickslides

So now use the assumption n=k to prove n=k+1

n=k $\displaystlye 1+4+9+\dots +k^2 = \frac{k(k+1)(2k+1)}{6}$

n=k+1 $\displaystlye 1+4+9+\dots +k^2 +(k+1)^2$

Using n=k for n=k+1 $\displaystlye 1+4+9+\dots +k^2 +(k+1)^2 = \frac{k(k+1)(2k+1)}{6}+(k+1)^2=\dots$
March 21st 2011, 06:55 PM
Archie Meade

However, to add to what pickslides has written,
you need to be aware of what you should end up with when you evaluate that sum!

You are attempting to show that

$\displaystyle\ 1+4+9+....+k^2+(k+1)^2=\frac{(k+1)(k+2)[2(k+1)+1]}{6}$

"if"

$\displaystyle\ 1+4+9+...+k^2=\frac{k(k+1)(2k+1)}{6}$

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