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

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

For the given statement Pn, write the statements P1, Pk, and Pk+1.
C) 2 + 4 + 6 + . . . + 2n = n(n+1)