MathDB

Pablo copied from the blackboard the problem: Consider all the sequences of

2004

real numbers

(x_0,x_1,x_2,\dots, x_{2003})

such that:

x_0=1, 0\le x_1\le 2x_0,0\le x_2\le 2x_1\ldots ,0\le x_{2003}\le 2x_{2002}

. From all these sequences, determine the sequence which minimizes

S=\cdots

As Pablo was copying the expression, it was erased from the board. The only thing that he could remember was that

S

was of the form

S=\pm x_1\pm x_2\pm\cdots\pm x_{2002}+x_{2003}

. Show that, even when Pablo does not have the complete statement, he can determine the solution of the problem.

Problem Statement