We will count the 7s among the thousands place digits,
then the hundreds place digits, then the tens place digits,
and finally the one-place digits.
There are no 7's among the thousands place digits.
Among the hundreds place digits,
700-799 account for 100 hundreds place 7s,
1700-1799 account for 100 hundreds place 7s,
2700-2710 account for 11 hundreds place 7s
That's 211 7s among the hundredths place digits.
70-79 account for 10 tens place 7s
170-79 account for 10 tens place 7s
...
2670-2679 account for 10 tens place 7s
That's 27x10=270 7s among the tens place digits.
[Note: from 2680 through 2710 there are no 7s in tens places.]
The 7s in ones digits occur in 7,17,27,37,...2697,2707
That's an arithmetic sequence with a1=7, an=2707, d=10
We find the number of terms:
Sum total= 211+270+271=752
There are 752 7s in all the page numbers.
Edwin
