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JEE Advanced Mathematics question

MathematicsBinomial TheoremJEE Advanced

The value of is equal to

Answer: (A)

Solution

Write and apply Pascal's rule repeatedly:

{}^{n+1}+{}^{n+1}={}^{n+2}, {}^{n+2}+{}^{n+2}={}^{n+3},\ ,\ {}^{2n}+{}^{2n}={}^{2n+1} .

So the sum telescopes to .

*Book's method:* ${}^{n+

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Question ID VK-110090