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Omni-MATH / For any finite set S, let f(S) be the sum of the elements of S (if S is empty then f(S)=0). Find the sum over all subsets E of S of (f(E))/(f(S)) for S={1,2,…,1999}.

Problem

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problem

For any finite set SS, let f(S)f(S) be the sum of the elements of SS (if SS is empty then f(S)=0f(S)=0). Find the sum over all subsets EE of SS of f(E)f(S)\frac{f(E)}{f(S)} for S={1,2,…,1999}S=\{1,2, \ldots, 1999\}.
Plain-text mathematical notation (without MathML)
For any finite set S, let f(S) be the sum of the elements of S (if S is empty then f(S)=0). Find the sum over all subsets E of S of (f(E))/(f(S)) for S={1,2,…,1999}.
Original LaTeX notation
For any finite set $S$, let $f(S)$ be the sum of the elements of $S$ (if $S$ is empty then $f(S)=0$). Find the sum over all subsets $E$ of $S$ of $\frac{f(E)}{f(S)}$ for $S=\{1,2, \ldots, 1999\}$.

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Source and history

task_id
0a8a389e-30a8-54fd-886b-c740caa8e07f
task_key
test--0a8a389e-30a8-54fd-886b-c740caa8e07f
task_revision_id
1
config / split
/ test

Official source

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