Sum of first 20 terms of ` 3/1^2 + 5/(1^2 + 2^2) + 7/(1^2 + 2^2 + 3^2) – InterviewSolution

1.	Sum of first 20 terms of ` 3/1^2 + 5/(1^2 + 2^2) + 7/(1^2 + 2^2 + 3^2) `+... upto 20 terms is :
Answer» `T_n=(2n+1)/(n(n+1)(2n+1)` `=6/(n(n+1)` `=6(1/n-1/(n+1))` `T_1=6(1-1/2)` `T_2=6(1/2-1/3)` `T_3=6(1/3-1/4)` `t_20=6(1/20-1/21)` `T_1+T_2+T_3...T_20=6(1-1/21)` `=6*20/21=40/7`.

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