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