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

20th sum

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Asked by lovemaan5500 3rd June 2018, 12:59 PM
Answered by Expert
Answer:
begin mathsize 16px style straight T subscript straight r plus 1 end subscript equals straight C presuperscript straight n subscript straight r straight a to the power of straight n minus straight r end exponent straight b to the power of straight r for open parentheses 1 plus straight a close parentheses to the power of straight n put space straight a equals 1 comma space straight b equals space straight a straight T subscript straight r plus 1 end subscript equals straight C presuperscript straight n subscript straight r space straight a to the power of straight r coefficient space of space left parenthesis straight r plus 1 right parenthesis to the power of th space term space is space straight C presuperscript straight n subscript straight r space For space straight r to the power of th space term space of space open parentheses 1 plus straight a close parentheses to the power of straight n put space straight r equals straight r minus 1 coefficient space of space straight r to the power of th space term space is space straight C presuperscript straight n subscript straight r minus 1 end subscript space For space left parenthesis straight r minus 1 right parenthesis to the power of th space term space of space open parentheses 1 plus straight a close parentheses to the power of straight n put space straight r equals straight r minus 2 coefficient space of space straight r to the power of th space term space is space straight C presuperscript straight n subscript straight r minus 1 end subscript space straight T subscript straight r minus 1 end subscript equals straight C presuperscript straight n subscript straight r minus 2 end subscript space straight a to the power of straight r minus 2 end exponent coefficient space of space left parenthesis straight r minus 1 right parenthesis to the power of th space term space is space straight C presuperscript straight n subscript straight r minus 2 end subscript since space left parenthesis straight r minus 1 right parenthesis comma straight r comma left parenthesis straight r plus 1 right parenthesis space are space in space ratio space 1 space colon space 7 space colon space 42 fraction numerator straight C presuperscript straight n subscript straight r minus 2 end subscript over denominator straight C presuperscript straight n subscript straight r minus 1 end subscript end fraction equals 1 over 7 fraction numerator begin display style fraction numerator straight n factorial over denominator left parenthesis straight r minus 2 right parenthesis factorial left parenthesis straight n minus left parenthesis straight r minus 2 right parenthesis right parenthesis factorial end fraction end style over denominator fraction numerator straight n factorial over denominator left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus left parenthesis straight r minus 1 right parenthesis right parenthesis factorial end fraction end fraction equals 1 over 7 fraction numerator open parentheses straight r minus 1 close parentheses over denominator open parentheses straight n minus straight r plus 2 close parentheses end fraction equals 1 over 7 straight n minus 8 straight r plus 9 equals 0....... left parenthesis 1 right parenthesis space Also space space space space fraction numerator straight C presuperscript straight n subscript straight r minus 1 end subscript over denominator straight C presuperscript straight n subscript straight r end fraction equals 7 over 42 fraction numerator begin display style fraction numerator straight n factorial over denominator left parenthesis straight r minus 1 right parenthesis factorial left parenthesis straight n minus left parenthesis straight r minus 1 right parenthesis right parenthesis factorial end fraction end style over denominator fraction numerator straight n factorial over denominator left parenthesis straight r right parenthesis factorial left parenthesis straight n minus 1 right parenthesis factorial end fraction end fraction equals 7 over 42 fraction numerator straight r over denominator straight n plus 1 minus straight r end fraction equals 1 over 6 6 straight r equals straight n plus 1 minus straight r...... left parenthesis 2 right parenthesis solving space left parenthesis 1 right parenthesis space and left parenthesis 2 right parenthesis straight r equals 8 space and space straight n equals 55 end style
Answered by Expert 4th June 2018, 11:37 AM
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