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).
See the text that illustrates the principle of mathematical induction using an infinite ladder.
2 + 4 + 8 + · · · + 2n = 2n+1 – 2
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