Binomial Summations #4 #Challenge

Geometry Level 5

If \(a\), \(b\) and \(c\) are the sides opposite to angles \(\widehat A\), \(\widehat B\) and \(\widehat C\) respectively of a triangle \(ABC\). Find the value of \[\Large \sum_{r=0}^{n} \left[\binom nr a^rb^{n-r}\cos\left(r\widehat B - (n-r)\widehat A\right)\right]\]

Here, take \(c = 1.194\) and \(n=50\). Also \(\widehat {ABC}\) represents \(\angle ABC\)

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