thank you sir!!!! but in the first one,, if we have to find 1/x then why n-r =1 why not n-r=-1 And answer is (2n)!/ [(n-1)!(n+1)!]

Asked by Nirbhay | 6th Nov, 2014, 09:42: AM

Expert Answer:

I space h a v e space m a d e space t h e space r e q u i r e d space c h a n g e s space i n space t h e space e a r l i e r space s o l u t i o n comma space p l e a s e space c h e c k space i t space o u t. I f space t h e space q u e s t i o n space i s space left parenthesis x plus 1 right parenthesis to the power of n open parentheses 1 plus 1 over x close parentheses to the power of n comma space t h e n space i t space c a n space b e space w r i t t e n space a s space fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 n end exponent over denominator x to the power of n end fraction comma space T h e space left parenthesis r plus 1 right parenthesis t h space t e r m space o f space fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 n end exponent over denominator x to the power of n end fraction space i s comma t subscript r plus 1 end subscript equals to the power of 2 n end exponent C subscript r x to the power of 2 n minus r end exponent over x to the power of n equals to the power of 2 n end exponent C subscript r x to the power of n minus r end exponent T o space f i n d space t h e space c o e f f i c i e n t space o f space 1 over x comma space x to the power of n minus r end exponent equals x to the power of minus 1 end exponent r equals n plus 1 C o e f f i c i e n t space o f space 1 over x space i s space to the power of 2 n end exponent C subscript n plus 1 end subscript equals fraction numerator left parenthesis 2 n right parenthesis factorial over denominator left parenthesis n minus 1 right parenthesis factorial left parenthesis n plus 1 right parenthesis factorial end fraction W h i c h space i s space t h e space a n s w e r space a s space g i v e n space b y space y o u space a b o v e.

Answered by Prasenjit Paul | 7th Nov, 2014, 10:33: AM

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