MathDB

Problem 3, Inequality with Integral

Source:

October 29, 2017

inequalitiescalculusintegration

Problem Statement

3. Let n > 1 be an integer and

a_1, a_2, . . . , a_n

be positive reals with sum 1. a) Show that there exists a constant c ≥ 1/2 so that

\sum \frac{a_k}{1+(a_0+a_1+...+a_{k-1})^2}\geq c

, where

a_0 = 0

. b) Show that ’the best’ value of c is at least

\frac{\pi}{4}