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Home / Doubts and Solutions/ICSE/Class 11 Science/Mathematics

Could u pls solve no.(30)

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Asked by pukai7229 10th November 2018, 9:59 AM
Answered by Expert
Answer:
Coefficient of xr-1 , xr and xr+1 are respectively begin mathsize 12px style C presuperscript n subscript r minus 1 end subscript space comma space C presuperscript n subscript r space a n d space C presuperscript n subscript r plus 1 end subscript space r e s p e c t i v e l y end style.
If these coefficients are in arithmatic progression, then we have
begin mathsize 12px style 2 space C presuperscript n subscript r space equals space C presuperscript n subscript r minus 1 end subscript space plus space C presuperscript n subscript r plus 1 end subscript 2 fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial space r factorial end fraction space equals space fraction numerator n factorial over denominator left parenthesis n minus r plus 1 right parenthesis factorial space left parenthesis r minus 1 right parenthesis factorial end fraction space plus space fraction numerator n factorial over denominator left parenthesis n minus r minus 1 right parenthesis factorial space left parenthesis r plus 1 right parenthesis factorial end fraction space.............. left parenthesis 1 right parenthesis i f space w e space m u l t i p l y space e q n. left parenthesis 1 right parenthesis space t h r o u g h o u t space b y space fraction numerator left parenthesis n minus r right parenthesis factorial space r factorial over denominator n factorial end fraction comma space w e space g e t 2 space equals fraction numerator r over denominator open parentheses n minus r plus 1 close parentheses end fraction space plus space fraction numerator open parentheses n minus r close parentheses over denominator open parentheses r plus 1 close parentheses end fraction space............ left parenthesis 2 right parenthesis end style
By simplifying equation (2), we get the required expression in the question
Answered by Expert 16th November 2018, 1:27 AM
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