Math, asked by ommrastogi, 9 months ago

By us9ng principal of mathematics induction prove: 2+2^2+2^3......2^n =2(2^n-1)

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Answered by vruddhi57
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Answered by Shivamrajprince
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The principle of mathematical induction

Let P(n) be a given statement involving the natural number n such that

Let P(n) be a given statement involving the natural number n such that (i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural

Let P(n) be a given statement involving the natural number n such that (i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural number) and

Let P(n) be a given statement involving the natural number n such that (i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural number) and (ii) If the statement is true for n = k (where k is a particular but arbitrary natural

Let P(n) be a given statement involving the natural number n such that (i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural number) and (ii) If the statement is true for n = k (where k is a particular but arbitrary natural number), then the statement is also true for n = k + 1, i.e, truth of P(k) implies

Let P(n) be a given statement involving the natural number n such that (i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural number) and (ii) If the statement is true for n = k (where k is a particular but arbitrary natural number), then the statement is also true for n = k + 1, i.e, truth of P(k) implies the truth of P(k + 1). Then P(n) is true for all natural numbers n.

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