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Omni-MATH / Given positive integers k,m,n such that 1≤k≤m≤n. Evaluate

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Given positive integers

k, m, n

such that

1 \leq k \leq m \leq n

. Evaluate

\sum^{n}_{i=0} \frac{(-1)^i}{n+k+i} \cdot \frac{(m+n+i)!}{i!(n-i)!(m+i)!}.

Plain-text mathematical notation (without MathML)

Given positive integers k,m,n such that 1≤k≤m≤n. Evaluate

∑_(i=0)^(n)((−1)^(i))/(n+k+i)⋅((m+n+i)!)/(i!(n−i)!(m+i)!).

Original LaTeX notation

Given positive integers $k, m, n$ such that $1 \leq  k \leq  m \leq  n$. Evaluate

\[\sum^{n}_{i=0} \frac{(-1)^i}{n+k+i} \cdot \frac{(m+n+i)!}{i!(n-i)!(m+i)!}.\]

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Source and history

task_id: 05d97329-05a5-5f80-aa88-4d3535e1ffac
task_key: test--05d97329-05a5-5f80-aa88-4d3535e1ffac
task_revision_id: 2
config / split: / test

Official source

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