1.

If \[|x|<1\], then the value of\[1+n\left( \frac{2x}{1+x} \right)+\frac{n(n+1)}{2!}{{\left( \frac{2x}{1+x} \right)}^{2}}+.....\infty \]will be [AMU 1983]

A. \[{{\left( \frac{1+x}{1-x} \right)}^{n}}\]
B. \[{{\left( \frac{2x}{1+x} \right)}^{n}}\]
C. \[{{\left( \frac{1+x}{2x} \right)}^{n}}\]
D. \[{{\left( \frac{1-x}{1+x} \right)}^{n}}\]
Answer» B. \[{{\left( \frac{2x}{1+x} \right)}^{n}}\]


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