MathDB
2016 Guts #19

Source:

December 24, 2016

Problem Statement

Let A=lim⁡n→∞∑i=02016(−1)i⋅(ni)(ni+2)(ni+1)2 A = \lim_{n \rightarrow \infty} \sum_{i=0}^{2016} (-1)^i \cdot \frac{\binom{n}{i}\binom{n}{i+2}}{\binom{n}{i+1}^2} Find the largest integer less than or equal to 1A\frac{1}{A}.
The following decimal approximation might be useful: 0.6931<ln⁡(2)<0.6932 0.6931 < \ln(2) < 0.6932, where ln⁡\ln denotes the natural logarithm function.
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