Use mathematical induction to prove the statement is true

Question

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

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

b) 1² + 4² + 7²+ ... + (3n-2)² = n(6n²-3n-1)/2

For the given statement P_n, write the statement P₁, P_k and P_k+1.

c) 2 + 4 + 6 + .. + 2n = n(n+1)