Prove by induction the inequality `(1+x)^ngeq 1+n x` whenever `x` is positive and `n` is a positive integer.

Explanation

Let p(n) be the statement given by

`P(n)=(2+x)^n≥1+nx`

For` n=1,P(1)=(1+x)^1≥1+x`


`1+x=1+x`

∴P(1)is true.

let us assume that , P(k) is true for some natural number k.

Then `P(k)=(1+x)^k≥1+kx`

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