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Find the sum of the series : (1 2 /1)+(1 2 +2 2 /1+2)+(1 2 +2 2 +3 2 /1+2+3)+………upto 31 terms.

Find the sum of the series : (12/1)+(12+22/1+2)+(12+22+32/1+2+3)+………upto 31 terms.


 

Grade:12

1 Answers

Pratik Tibrewal
askIITians Faculty 37 Points
9 years ago
r th term of the series is: SUM(r^2) / SUM(r) where SUM is summation from r = 1 to r

SUM(r^2) = r(r+1)(2r+1)/6
SUM(r) = r(r+1)/2
SUM(r^2)/SUM(r) = (2r+1)/3

we have to find SUM((2r+1)/3) where r varies from 1 to 31
SUM ((2r+1)/3) = 2(n(n+1)/6) + n/3
Put n = 31
Ans
343



Thanks and Regards,
Pratik Tibrewal
askiitians faculty
BTech IITG



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