Use mathematical induction to prove that the given statement is true for every p

Question

Use mathematical induction to prove that the given statement is true for every positive integer n. 1 + 2 + 22 + 23 + 24 + + 2n-1 = 2n - 1 When n = 1, both sides of the equation are equal to ; thus the statement is true. Assume that the statement is true for n = k. Then 1 + 2 + 22 + 23 + 24 + ... + 2k-1 = . Add 2k to both sides of the equation to get 1 + 2 + 22 + 23 + 24 + ... + 2k-1 + 2k = 2k - 1 +2k Thus, the statement is for n = k + 1. Therefore, by the Principle of Mathematical Induction, the statement is for all positive integers n.

Explanation / Answer

0 2^k-1 2^(k-1) true I am 100% sure abt the answer

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