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  4. The coefficient of x4 in ((1+x/1-x))2,|x|<1, is

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Q. The coefficient of $x^4$ in $\left(\frac{1+x}{1-x}\right)^2,|x|<1$, is

Binomial Theorem

Solution:

$ (1+x)^2(1-x)^{-2} $
$ =\left(1+x^2+2 x\right)(1-x)^{-2}$
Co-efficient of $x ^4={ }^5 C _4+{ }^3 C _2+2{ }^4 C _3=16$