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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?

 Nov 12, 2021
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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

 Nov 12, 2021

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