MathDB

Given integer

n\geq 2

. Find the minimum value of

\lambda {}

, satisfy that for any real numbers

a_1

a_2

\cdots

{a_n}

and

{b}

\lambda\sum\limits_{i=1}^n\sqrt{|a_i-b|}+\sqrt{n\left|\sum\limits_{i=1}^na_i\right|}\geqslant\sum\limits_{i=1}^n\sqrt{|a_i|}.

P21