Question

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.

1) 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 4(4n+1)(8n+7)/6

2) 1^2 + 4^2 + 7^2 + ... + (3n - 2)^2 = n(6n^2-3n-1)/2

Answer 1

Check to see whether the first equation holds for \(n=1\).