I know I could start multiplying by all denominators and try to get the exact value that way but is there some smarter way or shortcut?
Let's take simple example: $\displaystyle \frac{1}{99}+\frac{1}{98}+...+1$. How to approximate or to get the exact value fast?
I know I could split the sequence into sum of geometric series like $s_{2}=\frac{1}{2}+\frac{1}{4}+...=2,\qquad s_{3}=\frac{1}{3}+\frac{1}{9}+...=\frac{3}{2},$ but there can be an infinite amount of them if $Max$ is infinite.