MathDB

28

Part of 2014 Harvard-MIT Mathematics Tournament

Problems(1)

2014 Guts #28: Extension of Standard Polynomial Problem

Source:

8/26/2014
Let f(n)f(n) and g(n)g(n) be polynomials of degree 20142014 such that f(n)+(−1)ng(n)=2nf(n)+(-1)^ng(n)=2^n for n=1,2,…,4030n=1,2,\ldots,4030. Find the coefficient of x2014x^{2014} in g(x)g(x).
algebrapolynomialbinomial theorem