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
![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](https://images.topperlearning.com/topper/tinymce/cache/a0f0e310ea47e8b37ebd858013ef1f7b.png)
Answered by Arun | 13 May, 2019, 09:57: AM
Application Videos
Concept Videos
CBSE 12-science - Maths
Asked by pranavbhu249 | 12 Jul, 2024, 21:53: PM
CBSE 12-science - Maths
Asked by chinnuambichinnuambi | 12 Jun, 2024, 19:07: PM
CBSE 12-science - Maths
Asked by nirbhaysingh16102004 | 12 Jun, 2024, 10:04: AM
CBSE 12-science - Maths
Asked by niharika198two | 11 Jun, 2024, 11:36: AM
CBSE 12-science - Maths
Asked by gunguncutem4 | 07 Jun, 2024, 20:02: PM
CBSE 12-science - Maths
Asked by dharnidharni278 | 06 Jun, 2024, 18:30: PM
CBSE 12-science - Maths
Asked by eswarvajrapu | 06 Jun, 2024, 00:37: AM
CBSE 12-science - Maths
Asked by laksitaprakash17 | 31 May, 2024, 23:10: PM
CBSE 12-science - Maths
Asked by anushkashr4 | 29 May, 2024, 09:09: AM