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.
Help would be greatly appreciated Thank you
So now use the assumption n=k to prove n=k+1
n=k $\displaystyle \displaystlye 1+4+9+\dots +k^2 = \frac{k(k+1)(2k+1)}{6}$
n=k+1 $\displaystyle \displaystlye 1+4+9+\dots +k^2 +(k+1)^2 $
Using n=k for n=k+1 $\displaystyle \displaystlye 1+4+9+\dots +k^2 +(k+1)^2 = \frac{k(k+1)(2k+1)}{6}+(k+1)^2=\dots $
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
$\displaystyle \displaystyle\ 1+4+9+....+k^2+(k+1)^2=\frac{(k+1)(k+2)[2(k+1)+1]}{6}$
"if"
$\displaystyle \displaystyle\ 1+4+9+...+k^2=\frac{k(k+1)(2k+1)}{6}$