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CBSE Class 12-science Answered

  find the sum of the following series: S = 7/6 + 13/12 + 21/20 +31/30 +............. + 9901/9900 A) 9749/100 B) 9849/100 C) 9949/100 D) 9649/100
Asked by Ranjeetgupta26068 | 12 May, 2019, 01:04: AM
answered-by-expert Expert Answer
if space we space see space the space denominators comma 6 equals 2 cross times 3 13 equals 3 cross times 4 20 equals 4 cross times 5 and space numerators space are 7 equals 2 cross times 3 plus 1 13 equals 3 cross times 4 plus 1 21 equals 4 cross times 5 plus 1 so space it space is space of space the space form space straight a subscript straight n equals fraction numerator open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses plus 1 over denominator open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses end fraction straight a subscript straight n equals open parentheses 1 plus fraction numerator 1 over denominator open parentheses open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses close parentheses end fraction close parentheses straight a subscript straight n equals open parentheses 1 plus fraction numerator straight n plus 2 minus open parentheses straight n plus 1 close parentheses over denominator open parentheses open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses close parentheses end fraction close parentheses straight a subscript straight n equals open parentheses 1 plus 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 finding space number space of space terms 1 plus fraction numerator 1 over denominator open parentheses open parentheses straight n plus 1 close parentheses open parentheses straight n plus 2 close parentheses close parentheses end fraction equals 9901 over 9900 straight n equals 98 sum from straight n equals 1 to 98 of open parentheses 1 plus 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 equals 98 plus open parentheses 1 half minus 1 third plus 1 third minus 1 fourth plus...... plus 1 over 99 minus 1 over 100 close parentheses equals 98 plus open parentheses 1 half minus 1 over 100 close parentheses equals 9849 over 100
Answered by Arun | 13 May, 2019, 09:57: AM

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