Question

Prove that 2n > n for all positive integers n by the Principle of Mathematical Induction

Answer 1

Answer:

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Step-by-step explanation:

Let P(n):2n>n

When n=1,21>1.Hence P(1) is true.

Assume that P(k) is true for any positive integer k,i.e.,

2k>k 

we shall now prove that P(k+1) is true whenever P(k) is true.

Multiplying both sides of (1) by 2, we get

2.2k>2k

i.e., 2k+1>2k

k+k>k+1

∴2k+1>k+1