Question

If √(1 + 1/12 + 1/22) + √(1 + 1/22 + 1/32) + √(1 + 1/32 + 1/42) + ..... + √(1 + 1/(1999)2 + 1/(2000)2) = x - 1/x, then find the value of x.

Answer 1

Tr = √(1 + 1/r2 + 1/(r + 1)2)

x = 2000, - 1/2000