Write out in full and verify the statements S₁, S₂, S₃, S₄, and S₅ for the following. Then use mathematical induction to prove that each statement is true for every positive integer n.

2 + 4 + 6 + · · · + 2n = n(n + 1)

Let S_n represent the given statement, and use mathematical induction to prove that S_n is true for every positive integer n. Follow these steps.
(a) Verify S₁. 

(b) Write S_k . 

(c) Write _Sk+1.
(d) Assume that S_k is true and use algebra to change S_k to S_k+1.
(e) Write a conclusion based on Steps (a) – (d).