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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

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

!

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