CBSE Class 11-science Answered

$P r o v e space t h a t space t h e space c o e f f i c i e n t space o f space x to the power of p space i n space t h e space e x p a n s i o n space o f space open parentheses x squared plus 1 over x close parentheses to the power of 2 n end exponent space i s fraction numerator left parenthesis 2 n right parenthesis factorial over denominator left parenthesis fraction numerator p plus 2 n over denominator 3 end fraction right parenthesis factorial left parenthesis begin display style fraction numerator 4 n minus p over denominator 3 end fraction end style right parenthesis factorial end fraction$ Please provide solution to this question

Asked by Topperlearning User | 08 Oct, 2016, 03:12: PM

Expert Answer

$L e t space t h e space c o e f f i c i e n t space o f space x to the power of p space i s space i n space left parenthesis r plus 1 right parenthesis to the power of t h end exponent space t e r m space s o t subscript r plus 1 end subscript equals C presuperscript 2 n end presuperscript subscript r x to the power of 2 r end exponent left parenthesis 1 over x right parenthesis to the power of 2 n minus r end exponent p o w e r space o f space x space i n space t subscript r plus 1 space end subscript space s h o u l d space b e space e q u a l space t o space p space s o 2 r minus left parenthesis 2 n minus r right parenthesis equals p r equals fraction numerator 2 n plus p over denominator 3 end fraction c o e f f i c i e n t space o f space x to the power of p space i s space C presuperscript 2 n end presuperscript subscript fraction numerator 2 n plus p over denominator 3 end fraction end subscript equals fraction numerator left parenthesis 2 n right parenthesis factorial over denominator left parenthesis fraction numerator p plus 2 n over denominator 3 end fraction right parenthesis factorial left parenthesis begin display style fraction numerator 4 n minus p over denominator 3 end fraction end style right parenthesis factorial end fraction$