, 2014

Let $n\ge1$ be a fixed integer. Calculate the distance $\$\inf_{p,f} \max_{0\le x\le}$ 1} $\big|f(x)-p(x)\big|$$, where$p runs over polynomials of degree less than n with real coefficients and f$runs over functions$f(x) = $\sum_{k=n}^\infty$ c_k x^k$defined on the closed interval$[0,1]$, where$$c_k\ge0$$and$$\sum_{k=n}^\infty$ c_k=1$.
Miklós Schweitzer competition, 2014
(5 pont)