Northeastern WOOTers Mock AIME I Problems/Problem 8

Problem

Dai the Luzon bleeding-heart has numbered lillypads, $1$ through $100$. Then, Ryan the alligator eats those lillypads with the intention of eating Dai. Dai starts on a random lillypad and flies around between lillypads randomly every minute. Ryan also eats a random lillypad every minute. If the expected number of minutes left for Dai to live is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find $m+n$.

Solution

101/2 ---> 103

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