You start by correctly stating the problem!
How on earth are you supposed to see that "13" is NOT thirteen, but rather "1^3"?!?!
You can prove that the sum of the first n cubes is the square of the sum of the first n squares, btw...
I am completely aware of what I need to be doing to prove something by induction, except my algebra skills are too crappy to do it.
For example
prove the following by induction...
1^3 + 2^3 + 3^3 + ... + n3 = n^2(n+1)^2/4
I have already proved this is the case for n=1 and n=2
Then I say suppose it holds for n=k where k>=1
k^2(k+1)^2/4
Then I have to show it holds for k+1
So I have to show that....
(k+1)^2[(k+1)+1]^2/4 = k^2(k+1)^2/4 + (k+1)^2
Is this correct?
If it is how do i even start here. I noticed that they both have a (k+1)^2 term so i started by pulling that out front. I just get so lost from there...
You start by correctly stating the problem!
How on earth are you supposed to see that "13" is NOT thirteen, but rather "1^3"?!?!
You can prove that the sum of the first n cubes is the square of the sum of the first n squares, btw...