What do we get if we add the digits of the integers from 1 to 99?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

The function \(S(n)\) is defined for positive integers \(n\) by \[S(n) = \text{sum of the digits of }n.\] For example, \(S(723) = 7+2+3=12\). The sum \[S(1) + S(2) + S(3) + \dots + S(99)\] equals

1. \(746\),

2. \(862\),

3. \(900\),

4. \(924\).

Could we lay out the \(S\) values in a table?

How often does the digit \(1\) appear in the numbers from \(1\) to \(99\)?

What about the other digits?