GIVEN term can be WRITTEN as \[{{(1+X)}^{2}}{{(1-x)}^{-2}}\] \[=(1+2x+{{x}^{2}})[1+2x+3{{x}^{2}}+....+(n-1){{x}^{n-2}}\] \[={{x}^{n}}(n+1+2n+n-1)+....\] THEREFORE coefficient of \[{{x}^{n}}\] is 4n. "> GIVEN term can be WRITTEN as \[{{(1+X)}^{2}}{{(1-x)}^{-2}}\] \[=(1+2x+{{x}^{2}})[1+2x+3{{x}^{2}}+....+(n-1){{x}^{n-2}}\] \[={{x}^{n}}(n+1+2n+n-1)+....\] THEREFORE coefficient of \[{{x}^{n}}\] is 4n. ">
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In the expansion of \[{{\left( \frac{1+x}{1-x} \right)}^{2}}\], the coefficient of \[{{x}^{n}}\] will be

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 11 months ago

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GIVEN term can be WRITTEN as \[{{(1+X)}^{2}}{{(1-x)}^{-2}}\] \[=(1+2x+{{x}^{2}})[1+2x+3{{x}^{2}}+....+(n-1){{x}^{n-2}}\] \[={{x}^{n}}(n+1+2n+n-1)+....\] THEREFORE coefficient of \[{{x}^{n}}\] is 4n.
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Posted on 10 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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