Difference between revisions of "AoPS Wiki talk:Problem of the Day/July 6, 2011"
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<math> n \le 9 </math>: <math>\boxed {123 ... n} </math> | <math> n \le 9 </math>: <math>\boxed {123 ... n} </math> | ||
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<math> 1+11+\cdots+\underbrace{111\cdots 111}_{n}} = n + 10(n-1) + 100(n-2) + \cdots + 10^{n-1}(n-(n-1)</math>. This can be expressed as the summation: | <math> 1+11+\cdots+\underbrace{111\cdots 111}_{n}} = n + 10(n-1) + 100(n-2) + \cdots + 10^{n-1}(n-(n-1)</math>. This can be expressed as the summation: | ||
<math>\boxed{\sum\limits_{k=0}^n 10^{k}(n-k)}</math> | <math>\boxed{\sum\limits_{k=0}^n 10^{k}(n-k)}</math> | ||
Revision as of 15:01, 6 July 2011
Problem
AoPSWiki:Problem of the Day/July 6, 2011
Solution
This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it.
Trivial Case
: 
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:
