- #1
cnwilson2010
- 8
- 0
Homework Statement
Prove:
1^3 + 2^3 +...+n^3=(1+2+...+n)^2
n=Natural number
Homework Equations
The Attempt at a Solution
Using induction -
n=1 obvious
Assume for n=k equation is true.
Show for k+1.
I have that the right side prior to k+1 is (k^2(k+1)^2)/4
After k+1 I have (k^4+6k^3+13k^2+12k+4)/4,
but I can't figure out the trick to get the form above equal to the left +(k+1)^3.
Any ideas?
Thanks.