Difference between revisions of "Random Problem"
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== Medium Problem == | == Medium Problem == | ||
| − | Show that there exist no finite decimals <math>a = 0.\overline{a_1a_2a_3\ldots a_n}</math> such that when its digits are rearranged to a different decimal <math>b = 0.\overline{ | + | Show that there exist no finite decimals <math>a = 0.\overline{a_1a_2a_3\ldots a_n}</math> such that when its digits are rearranged to a different decimal <math>b = 0.\overline{a_{b_1}a_{b_2}a_{b_3}\ldots a_{b_n}}</math>, <math>a + b = 1</math>. |
==Solution== | ==Solution== | ||
??? | ??? | ||
Revision as of 11:07, 30 January 2023
Easy Problem
The sum![\[\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\cdots+\frac{2021}{2022!}\]](http://latex.artofproblemsolving.com/7/2/6/726b88e230d5c0a0303ef6ca7177fa73b7eec900.png)
can be expressed as 
, where 
and 
are positive integers. What is 
?
Solution
???
Medium Problem
Show that there exist no finite decimals 
such that when its digits are rearranged to a different decimal 
, 
.
Solution
???
