Question

If the natural numbers are written as a sequence 12345678910111213141516...... then the 2007th digit is ????

Answer 1

Answer on Question #52401 – Math – Combinatorics | Number Theory

If the natural numbers are written as sequence 12345678910111213141516... then the 2007th digit is?

Solution

1-digit numbers - take 9 digits.

2-digit numbers - take $90 \cdot 2 = 180$ digits.

A1=10, an=99=a1+(n-1)=10

3-digit numbers - take $900 \cdot 3 = 2700$ digits.

So let find the 3-digit number, which has 2007th digit of our sequence:

$$9 + 180 + x \cdot 3 = 2007 \Rightarrow x = 606$$

where x - number of three-digit number beginning with 100.

So our 3-digit number, which has 2007th digit of our sequence is $606 + 100 - 1 = 705$.

According to equation, x is integer, our digit is the last number of x, it is 5.

**Answer:** 5.

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