# Prove the following by induction

• Nov 17th 2011, 11:26 AM
ehpoc
Prove the following by induction
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...
• Nov 17th 2011, 01:14 PM
TheChaz
Re: Prove the following by induction
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...
• Nov 17th 2011, 02:09 PM
ehpoc
Re: Prove the following by induction
sorry I never noticed when I copy and pasted

Quote:

You can prove that the sum of the first n cubes is the square of the sum of the first n squares, btw...
no clue what you are saying LOL
• Nov 17th 2011, 02:13 PM
Deveno
Re: Prove the following by induction
he is saying:

$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k^2\right)^2$

although this is incorrect, the actual formula is:

$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2$
• Nov 17th 2011, 04:34 PM
TheChaz
Re: Prove the following by induction
Quote:

Originally Posted by Deveno
he is saying:

$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k^2\right)^2$

although this is incorrect, the actual formula is:

$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2$

The latter is what I wanted to say! I lose track of my prepositional phrases sometimes :)