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AoPS Wiki talk:Problem of the Day/July 6, 2011

Revision as of 14:01, 6 July 2011 by Esque (talk | contribs) (→‎Solution)

Problem

AoPSWiki:Problem of the Day/July 6, 2011

Solution

Trivial Case

$n \le 9$: $\boxed {123 ... n}$

Solution

$1+11+\cdots+\underbrace{111\cdots 111}_{n}} = n + 10(n-1) + 100(n-2) + \cdots + 10^{n-1}(n-(n-1)$ (Error compiling LaTeX. Unknown error_msg). This can be expressed as the summation:

$\boxed{\sum\limits_{k=0}^n 10^{k}(n-k)}$

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