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For each number from 1 to 99, Andrew wrote down the sum of its digits. What is the mean of the numbers Andrew wrote down?

 Aug 15, 2020
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For each number from 1 to 99, Andrew wrote down the sum of its digits. What is the mean of the numbers Andrew wrote down?

 

Hello Guest!

 

 

\(\sum_{k=1}^n\ k=\frac{n^2+n}{2}\)

\(\sum_{k=1}^9\ k=\frac{9^2+9}{2}=45\)

 

The mean of the numbers from 1 to 99 is

 

\(\frac{10\cdot 45+9\cdot 45}{90+99}=\frac{855}{189}=\color{blue}4.\overline{523809}\)

 

laugh  !

 Aug 15, 2020
edited by asinus  Aug 15, 2020
edited by asinus  Aug 15, 2020

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