Zeros of a Log Taylor Polynomial

Problem

Let

f(x) = 1 + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots - \frac{x^{2014}}{2014} + \frac{x^{2015}}{2015}.

If every zero of $f(x)$ lies in an interval $[a, b]$ with $a < b$ and $a, b \in \mathbb{Z}$ , find the minimum value of $b - a$ .

Answer

Solution

Difficulty	7/10
Topics	calculus, Monotonicity, Polynomials

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