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limit of minimum of sum from k=0 to 2n of x_k

Source: Nordic Mathematical Contest 1988 #4

October 5, 2017
functionlimitminimum valuealgebra

Problem Statement

Let mnm_n be the smallest value of the function fn(x)=∑k=02nxk{{f}_{n}}\left( x \right)=\sum\limits_{k=0}^{2n}{{{x}^{k}}} Show that mn→12m_n \to \frac{1}{2}, as n→∞.n \to \infty.
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