what digit is in the sequence of natural numbers 12345... in the 500,000th place??
There are 9 numbers with 1 digit, then 90 with 2 digits (for a total of 180 digits), then 900 with 3 digits (2700 digits), and so on. The total number of digits in all numbers less than 100,000 is 9+180+2700+36,000+450,000 = 488,889. Then we start the six-digit numbers. So you are looking for the 500,000-488,889=11,111th digit in the numbers starting at 100,000. But each of these numbers has 6 digits, and 11,111=6×1851+5. Therefore you want the fifth digit in the number 101,851.