Question

GIVING A MEDAL! Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = (4(4n+1)(8n+7))/(6)

Answer 1

First show the statement holds for the base case (which looks like it would be n=1).

Answer 2

In other words, show that
\[4(1)(4(1)+2)=\frac{4(4(1)+1)(8(1)+7)}{6}\]