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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

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Asked by Topperlearning User 8th October 2016, 3:12 PM
Answered by 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

Answered by Expert 8th October 2016, 5:12 PM
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