Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 627. (November 2014)

A. 627. Let $\displaystyle n\ge1$ be a fixed integer. Calculate the distance $\displaystyle \inf_{p,f} \max_{0\le x\le 1} \big|f(x)-p(x)\big|$, where $\displaystyle p$ runs over polynomials of degree less than $\displaystyle n$ with real coefficients and $\displaystyle f$ runs over functions $\displaystyle f(x) = \sum_{k=n}^\infty c_k x^k$ defined on the closed interval $\displaystyle [0,1]$, where $\displaystyle c_k\ge0$ and $\displaystyle \sum_{k=n}^\infty c_k=1$.

Miklós Schweitzer competition, 2014

(5 pont)

Deadline expired on December 10, 2014.

### Statistics:

 3 students sent a solution. 5 points: Williams Kada. 3 points: 1 student. 0 point: 1 student.

Problems in Mathematics of KöMaL, November 2014