And show all work use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. (4 points each.) 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + + 4n( 4n + 2) = quantity four times quantity four n plus one times quantity eight n plus seven divided all divided by six 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = quantity n times quantity six n squared minus three n minus one all divided by two for the given statement pn, write the statements p1, pk, and pk+1. (2 points) 2 + 4 + 6 + . . + 2n = n(n+1)