What Pascal Identity Should I use?
Number Theory
Level
2
Let \(b_{k,n}\) be the \(k^\text{th}\) element of the \(n^\text{th}\) row of Pascal's triangle, with row \(1\) being \(\{1\},\) row \(2\) being \(\{1,1\},\) etc. Also, the \(1^\text{st}\) element of each row is \(1.\)
Find the value of
\[(b_{3,2015})^2 - \sum_{i=1}^{2013} i^3.\]
Details and Assumptions:
- For example, \(b_{1,1} = 1, b_{2,3} = 2,\) and \(b_{5,6} = 5.\)
Image Credit: Wikipedia Pascal Triangle
by
Caleb Townsend