Use Mathematical Induction to prove equation? Use mathematical induction to prove each of the following statements.
let $$g(n) = 1^3 + 2^3 + 3^3 + ... + n^3$$
Show that the function $$g(n)= \frac{n^2(n+1)^2}{4}$$ for all n in N
so the base case is just g(1) right? so the answer for the base case is 1, because 4/4 = 1
then for g(2) is it replace all of the n's with n + 1 and see if there is a concrete answer?

First, show that this is true for $n=1$:
$\sum\limits_{k=1}^{1}k^3=\frac{1^2(1+1)^2}{4}$
Second, assume that this is true for $n$:
$\sum\limits_{k=1}^{n}k^3=\frac{n^2(n+1)^2}{4}$
Third, prove that this is true for $n+1$:
$\sum\limits_{k=1}^{n+1}k^3=$
$\color\red{\sum\limits_{k=1}^{n}k^3}+(n+1)^3=$
$\color\red{\frac{n^2(n+1)^2}{4}}+(n+1)^3=$
$\frac{(n+1)^2(n+1+1)^2}{4}$

Please note that the assumption is used only in the part marked red.
