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Prove that the sum is less than 80 - n variables inequality

Source:

9/21/2010
Let MM be the set of all positive integers that do not contain the digit 99 (base 1010). If x1,…,xnx_1, \ldots , x_n are arbitrary but distinct elements in MM, prove that ∑j=1n1xj<80.\sum_{j=1}^n \frac{1}{x_j} < 80 .
decimal representationDigitsseries summationInequalityalgebraIMO Shortlist