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Omni-MATH / A counter begins at 0 . Then, every second, the counter either increases by 1 or…

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problem

A counter begins at 0 . Then, every second, the counter either increases by 1 or resets back to 0 with equal probability. The expected value of the counter after ten seconds can be written as mn\frac{m}{n}, where m,nm, n are positive integers and gcd(m,n)=1\operatorname{gcd}(m, n)=1. Find 100m+n100 m+n.
Plain-text mathematical notation (without MathML)
A counter begins at 0 . Then, every second, the counter either increases by 1 or resets back to 0 with equal probability. The expected value of the counter after ten seconds can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1. Find 100m+n.
Original LaTeX notation
A counter begins at 0 . Then, every second, the counter either increases by 1 or resets back to 0 with equal probability. The expected value of the counter after ten seconds can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100 m+n$.

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task_id
77c4f22c-a6c2-57ca-af8c-063ecfdb914b
task_key
test--77c4f22c-a6c2-57ca-af8c-063ecfdb914b
task_revision_id
1
config / split
/ test

Official source

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