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1 / a_1 + 1 / a_2 + \ldots + 1 / a_n = 1 , sum is <= n ^ {2 ^ n}

Source: Tuymaada Junior 2003 p4

May 11, 2019

algebraSummaximum valuemaximuminequalities

Problem Statement

The natural numbers

a_1

a_2

\dots

a_n

satisfy the condition

1 / a_1 + 1 / a_2 + \ldots + 1 / a_n = 1

. Prove that all these numbers do not exceed

n ^ {2 ^ n}