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 Sn represent the given statement, and use mathematical induction to prove that Sn is true for every positive integer n. Follow these steps.
(a) Verify S1.
(b) Write Sk .
(c) Write Sk+1.
(d) Assume that Sk is true and use algebra to change Sk to Sk+1.
(e) Write a conclusion based on Steps (a) – (d).
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