Problem: The number of diagonals that can be drawn in a polygon of 100100100 sides is:
Answer Choices:
A. 485048504850 B. 495049504950 C. 990099009900 D. 989898 E. 880088008800
Solution:
d=n(n−3)2=100(100−3)2=100(97)2=50⋅97=4850\begin{aligned} d &= \frac{n(n-3)}{2} \\ &= \frac{100(100-3)}{2} \\ &= \frac{100(97)}{2} \\ &= 50 \cdot 97 \\ &= \boxed{4850} \end{aligned} d=2n(n−3)=2100(100−3)=2100(97)=50⋅97=4850