Prove that 1 - xn- 1 - nx- for all natural number n- where x-1-

[ ( 1 + x)^n = 1 + ^nC_1x + ^nC_2x^2 + ^nC_3x^3 + .....; #160;= 1 + nx + x^2( ^nC_2 + ^nC_3x + .....) ] ≥( 1 + nx) for any natural no. ...

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Binomial Theorem

Prove that ...

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Prove that ${(1 + x)}^{n} \geq (1 + n x)$ , for all natural number $n$ , where $x > - 1$ .

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(1 + x)^{n} \geq (1 + n x)

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