How to calculate the sum for $\sum_{i=1}^{n} \frac{1}{n-i+1} \sqrt{\left( \sum_{r=0}^{i-1} \frac{n!}{r!(n-r)!}\left( p \right)^r \left( 1-p \right)^{n-r} \right)}$ when $n$ is finite? Any suggestion or references will be highly appreciated.
2026-03-31 12:49:41.1774961381
Sum of a series with square root
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