2007 IMO Shortlist Problems/A1: Difference between revisions
New page: == Problem == (''New Zealand'') You are given a sequence <math>a_1,a_2,\dots ,a_n</math> of numbers. For each <math>i</math> (<math>1\leq 1\leq n</math>) define <center><math>d_i=\max\{a_... |
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== Problem == | == Problem == | ||
(''New Zealand'') | (''New Zealand'') let's solve this problem bois @poco @john | ||
You are given a sequence <math>a_1,a_2,\dots ,a_n</math> of numbers. For each <math>i</math> (<math>1\leq 1\leq n</math>) define | You are given a sequence <math>a_1,a_2,\dots ,a_n</math> of numbers. For each <math>i</math> (<math>1\leq 1\leq n</math>) define | ||
Revision as of 20:24, 10 December 2019
Problem
(New Zealand) let's solve this problem bois @poco @john
You are given a sequence 
of numbers. For each 
(
) define
and let
.(a) Prove that for arbitrary real numbers 
,
.(b) Show that there exists a sequence of real numbers such that we have equality in (a).
Solution
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