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Grade 12Algebra

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

Profile image of Ranjeet Gupta
7 Years agoGrade 12
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1 Answer

Profile image of Aditya Gupta
ApprovedApproved Tutor Answer7 Years ago
consider the denominators 6, 12, 20, 30, ….
6= 2*3
12= 3*4
20= 4*5 etc
so the nth term of sequence is 
an= [1 + (n+1)(n+2)]/(n+1)(n+2) for eg if you find a4= 31/30 which is correct.
now write an= 1 + [1/(n+1)(n+2)]
= 1 + 1/(n+1) – 1/(n+2)
obviusly the sum of 1/(n+1) – 1/(n+2) TELESCOPES.
hence the sum on further simplification turns out to be 9849/100.
kindly approve :)

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