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**How many numbers containing the digit 1.Help!**

Hello,

The question i am dealing with is this:Considering the integers from 1 to 10,000,000,000, answer the following two questions:

A. Is the number of integers that include the digit 1 greater or less than the number of integers that do not include the digit 1?

B. What is the difference between number (quantity) of integers that include the digit 1 and the number of integers that do not include the digit 1?

a. There are 6513211999 that include 1 as a digit, and there are 3486788001 numbers that don’t contain digit of 1.

Therefore, there are more numbers that contain the digit 1 than not.

b.3026423998

Reasoning:

After some trials, i came up with the following recurrence relation:

[tex]a_1=19,.. a_2=100,.. a_{2n}=(10)^{n+1}.. and... a_{2n+1}=8*\sum _{i=1}^{2n-1} a_i[/tex]

Now the total sum of the numbers that contain digits is calculated by summing up the following:

[tex]a_{14}+\sum_{n=1}^{6}[a_{2n}+a_{2n+1}]=

=

a_{14}+\sum_{n=1}^{6}[ a_{2n}+(8*\sum _{i=1}^{11} a_i) ][/tex]

I don't know whether there is supposed to be a more clever and including less calculations method for doing this.

FIrst, is the answer correct? ANd second if yes, does my reasoning make sense?

THnx in advance!

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