Question

[Thạch Phạm Văn]

(1^2/1.3)+(2^2/3.5)+....+(n^2/(2n-1)(2n+1))=(n(n+1))/((2n-1)(2n+1))

Answer 1

[Die Devil]

Đặt A = 1/1.3 + 1/3.5 + 1/5.7 +........+ 1/(2n - 1)(2n + 1)
2.A = 2/1.3 + 2/3.5 + 2/5.7 +........+ 2/(2n - 1)(2n + 1)
2.A = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ..... + 1/(2n - 1) - 1/(2n + 1)
2.A = 1 - 1/(2n + 1) = 2n/(2n + 1)
Vậy A = n/(2n + 1)