[ Arithmetic progression ]

[ Arithmetic. Mental calculation, etc. ]

What is the sum of the digits of all numbers from one to a billion?
Add zero to these numbers and form 500 million pairs: (0, 999999 999), (1, 999999 998), and so on. In each pair, the sum of the digits is 81, and besides, we forgot the number 1000000 000; therefore, the total sum is $500000000 \times 81+1=40500000001$.

## Answer

40500000001.