# 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 $$\angle ABC$$

×