Proof involving Induction

Question

Prove that for every integer n ≥ 1, we have

$$ \sum_{i=1}^ni^3=\left(\frac{n(n+1)}2\right)^2 $$

Solve using Mathematical Induction, include the Inductive Step

Base Case is that both the left and right side $=1$ when $n=1$. and the Inductive Hypothesis is $1^3+2^3+\dots +k^3=\frac{\left( k(k+1)\right)^2}2$

Base Case is that both the left and right side =1 when n=1. and the Inductive Hypothesis is 1^3+2^3+…k^3=(k(k+1))^2/2 — Drew, Nov 14 '14 at 00:51

score 2 · Answer 1 · answered Nov 14 '14 at 00:49

2

Define $$ A_n = \frac{n^2(n+1)^2}4 $$ then what is $A_n - A_{n-1}$?

answered Nov 14 '14 at 00:49

mookid

1 Answers1