Question 6
Given $$\frac ab=\frac{1\frac 12\times 2\frac 23\times 3\frac 34\times\cdots\times 98\frac{98}{99}\times 99\frac{99}{100}}{1\times 2\times 3\times\cdots\times 99\times 100},$$ where $a/b$ is in lowest terms with positive integers $a,b$, find $a+b$.
