+1808 For a positive integer n, let
a_n = 1 + \sqrt{\frac{1}{n}} - \sqrt{\frac{1}{n + 1}
Compute the product a_1 a_2 a_3 \dotsm a_{99}.
+77 firstly, you realize that \(a_n = 1+1/n(n+1)\), which is \((n^2+n+1)/n^2+n\) No idea what to do next, just a idea!
