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By principle of mathematical induction, 24n-1 is divisible by which of the following?

By principle of mathematical induction, 24n-1 is divisible by which of the following? Correct Answer 8

P(n) = 24n – 1 P(1) = 23 = 8 Let us assume P(k) is divisible by 8 and can be written as 8c, where c is any integer. P(k) = 24k – 1 = 8c P(k + 1) = 24(k + 1) – 1 P(k + 1) = 24k + 3 P(k + 1) = 24 . 24k – 1 P(k + 1) = 24 . 8c Clearly, P(k + 1) is divisible by 2, 4, 8 and 16.

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