Question

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

Is the statement typed out correctly? When n = 1, the first term is indeed 4(1)(4(1)+2)=4*6, but when n = 2, you get 4(2)(4(2)+2)=8*10, not 5*7.