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 F i n d space t h e space v a l u e space o f space C presuperscript n subscript r plus C presuperscript n subscript r minus 1 end subscript

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Asked by Topperlearning User 8th October 2016, 1:07 PM
Answered by Expert
Answer:

C presuperscript n subscript r equals fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction
C presuperscript n subscript r minus 1 end subscript equals fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r plus 1 right parenthesis factorial end fraction
C presuperscript n subscript r plus C presuperscript n subscript r minus 1 end subscript equals fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction plus fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r plus 1 right parenthesis factorial end fraction equals fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r right parenthesis factorial end fraction open parentheses 1 over r plus fraction numerator 1 over denominator n minus r plus 1 end fraction close parentheses
equals fraction numerator n factorial over denominator left parenthesis r minus 1 right parenthesis factorial left parenthesis n minus r right parenthesis factorial end fraction open parentheses fraction numerator n plus 1 over denominator r left parenthesis n minus r plus 1 right parenthesis end fraction close parentheses
equals fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator r factorial left parenthesis n minus r plus 1 right parenthesis right parenthesis factorial end fraction equals C presuperscript n plus 1 end presuperscript subscript r

Answered by Expert 8th October 2016, 3:07 PM
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