Hey all,
can anyone show me how I can prove a statement like this by Induction. Thanks.
$\displaystyle 1^3+2^3+3^3+...+n^3=\frac{1}{4}n^2(n+1)^2$ for all $\displaystyle n \in \mathbb{Z}$
Well, your n is natural unzero. (the sum starts with 1)
Read this: Mathematical induction - Wikipedia, the free encyclopedia
First step - verify if for n=1 that equality is true.
Second step (Induction) - we (you) suppose that k verify the equality and prove that then k+1 verify too.
Hey,
Stuck on the Induction step where I must rewrite the left-hand side..
..(1^3+2^3+3^3+...+n^3)+(n^3+1)=1/4*(n^3+1)(n^3+2)^2
EDIT: Should be (1^3+2^3+3^3+...+n^3)+(n+1)=1/4*(n+1)^2((n+1)+1)^2 and is straight forward to prove from there. Thanks for the help..