Prove that 1-xn - 2n 1-n 1-x1-x -nn-11 - 2 1-x1-x2 -

Given LHS=(1+x)^n multiply and divide by 2 inside the bracket =2^n.(1+x2)^n denomenator can be manipulated as =2^n.(1+x1+x+1 x)^n =2^n.(1+x+1 ...

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Linear Equation in One Variable

Prove that ...

Question

Prove that $(1 + x)^{n} = 2^{n} {1 - n \frac{1 - x}{1 + x} + \frac{n (n + 1)}{1 \cdot 2} {(\frac{1 - x}{1 + x})}^{2} \cdot \cdot \cdot}$

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lim x \to 1 \frac{x + x^{2} + x^{3} + . . . . + x^{n} - n}{x - 1}

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\frac{d y}{d x} = \frac{1}{2 (1 + x^{2})}

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