If 2/3*3/4*4/5* ... * n/(n+1) = 1/500, what is the sum of the numerator and denominator of the largest fraction on the left side of the equation?

Solve for n: 2/(n + 1) = 1/500

Take the reciprocal of both sides: (n + 1)/2 = 500

Multiply both sides by 2: n + 1 = 1000

Subtract 1 from both sides: n = 999 and (n+1) ==1,000