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Asked by vikasg13.hardware | 28 Jun, 2018, 06:14: AM
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begin mathsize 16px style sum from straight n equals 1 to 9 of fraction numerator 1 over denominator straight n left parenthesis straight n plus 1 right parenthesis left parenthesis straight n plus 2 right parenthesis end fraction equals straight p over straight q 1 half begin inline style sum from straight n equals 1 to 9 of end style fraction numerator straight n straight n plus 2 minus straight n over denominator straight n left parenthesis straight n plus 1 right parenthesis left parenthesis straight n plus 2 right parenthesis end fraction equals fraction numerator begin display style straight p end style over denominator begin display style straight q end style end fraction begin inline style sum from straight n equals 1 to 9 of open parentheses begin display style fraction numerator 1 over denominator straight n left parenthesis straight n plus 1 right parenthesis end fraction end style minus begin display style fraction numerator 1 over denominator left parenthesis straight n plus 1 right parenthesis left parenthesis straight n plus 2 right parenthesis end fraction end style close parentheses equals end style fraction numerator begin display style 2 straight p end style over denominator begin display style straight q end style end fraction begin inline style sum from straight n equals 1 to 9 of end style open parentheses 1 over straight n minus fraction numerator 1 over denominator straight n plus 1 end fraction minus open parentheses fraction numerator 1 over denominator straight n plus 1 end fraction minus fraction numerator 1 over denominator straight n plus 2 end fraction close parentheses close parentheses equals fraction numerator begin display style 2 straight p end style over denominator begin display style straight q end style end fraction open parentheses 1 minus 1 half plus 1 half minus 1 third plus.... plus 1 over 9 minus 1 over 10 close parentheses begin inline style negative open parentheses begin display style 1 half end style minus begin display style 1 third end style plus begin display style 1 third end style minus begin display style 1 fourth end style plus.... plus begin display style 1 over 10 end style minus begin display style 1 over 11 end style close parentheses equals end style fraction numerator 2 straight p over denominator straight q end fraction straight q minus straight p equals 110 minus 27 straight q minus straight p equals 83 end style
Answered by Sneha shidid | 03 Jul, 2018, 12:09: PM

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