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Omni-MATH / Let f(n) and g(n) be polynomials of degree 2014 such that f(n)+(−1)^(n)g(n)=2^(n) for n=1,2,…,4030. Find the coefficient of x²⁰¹⁴ in g(x).

Problem

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problem

Let f(n)f(n) and g(n)g(n) be polynomials of degree 2014 such that f(n)+(−1)ng(n)=2nf(n)+(-1)^{n} g(n)=2^{n} for n=1,2,…,4030n=1,2, \ldots, 4030. Find the coefficient of x2014x^{2014} in g(x)g(x).
Plain-text mathematical notation (without MathML)
Let f(n) and g(n) be polynomials of degree 2014 such that f(n)+(−1)^(n)g(n)=2^(n) for n=1,2,…,4030. Find the coefficient of x²⁰¹⁴ in g(x).
Original LaTeX notation
Let $f(n)$ and $g(n)$ be polynomials of degree 2014 such that $f(n)+(-1)^{n} g(n)=2^{n}$ for $n=1,2, \ldots, 4030$. Find the coefficient of $x^{2014}$ in $g(x)$.

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Source and history

task_id
37f24d1a-c498-5012-96a3-2fb0dd0083fb
task_key
test--37f24d1a-c498-5012-96a3-2fb0dd0083fb
task_revision_id
1
config / split
/ test

Official source

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