1. ## Proof question

I have a question that's giving me a hard time and im not sure how to go about solving it...

Prove that 1^3 + 2^3 + ... + n^3 = [n(n+1)/2]^2 while n>= 1

im a little lost at what to do after testing it out for n = 1 and proving that true.

2. Originally Posted by JoeBabble
I have a question that's giving me a hard time and im not sure how to go about solving it...

Prove that 1^3 + 2^3 + ... + n^3 = [n(n+1)/2]^2 while n>= 1

im a little lost at what to do after testing it out for n = 1 and proving that true.
Mathematcal Induction

For P(1):

Put n=1
RHS =LHS
Hence our assumption is correct for n=1

Assumption P(K):

Let the above statement be correct for n=k
Hence

1^3 + 2^3 + ... + k^3 = [k(k+1)/2]^2.............................1

Prove it For P(k+1):

So LHS will be

1^3 + 2^3 + ... + k^3 + (k+1)^3

Now for terms till n=k put the values obtained in (1)

[k(k+1)/2]^2 + (k+1)^3

On simplifying the above thing you will get

[(k+1)(k+2)/2]^2

This proves that the statement is correct for n = (k+1) when its correct for n= k

Hence through the principle of mathematical induction we have proved that the statement is correct