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Find the sum upto n terms. 1/3 + 2/21 + 3/91 + ..........

Find the sum upto n terms. 1/3 + 2/21 + 3/91 + ..........

Grade:11

1 Answers

Faiz
107 Points
7 years ago
-> 1/1*3 + 2/3*7 + 3/7*13 ... For eveey denom. first terms Let a= 1+ 3 + 7... Nth term for it will be n²-n+1 For every denom. second terms Let b= 3 + 7 + 13.... Nth term for it will be n²+n+1 Combining we get nth term of the series T= n / (n²-n+1)(n²+n+1) Which can be broken as: T= 1/2 [ 1/n²-n+1 - 1/n²+n+1] Now put values starting from 1,2,3... And add alll.. Sum= 1/2 [ 1- 1/n²+n+1] Sum= 1/2 ( n(n+1) / n²+n+1 )

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