(1111) 2 multiplied by (111) 2 vertical? Binary!

(1111) 2 multiplied by (111) 2 vertical? Binary!

Formula:
one thousand one hundred and eleven
111 x
-----------------
one thousand one hundred and eleven
one thousand one hundred and eleven
one thousand one hundred and eleven
---------------
1101001 =105

In the sum of 1 + 11 + 111 + 1111 +. + 111.. 1111 (the last one in 2009), how many times does the number 1 appear

Because 111... 1 (n 1) = 999... 9 (n 9) / 9 = (10 ^ n-1) / 9
So the original form
(10-1) / 9 + (100-1) / 9 + (1000-1) / 9 +... + (1000... 0 (2009 0) - 1) / 9
=111... 1 (2009 1) 0 / 9-2009 / 9
=111... 1 (2005 1) 09101 / 9
=123456790 123456790 123456790... (2005 / 9 = 222... 7; 222 group) 12345678789 (from 111111109101 / 9)
So there are 222 + 2 = 224 1

Find the law: one 5,11,23, (), 65, (). Two 8,2,10,4,12,6, (), ()

One
5,、11、23、（41）、65、（95）；
Principle:
11-5=6
23-11=12
41-23=18
65-41=24
95-65=30
An arithmetic sequence with a tolerance of 6
two
8、2、10、4、12、6、（14）（8）
From the other side,
8,10,12,14
2,4,6,8 (2 more each time)

-2-5-11-23

-2 -5 -11 -23 -47
Subtracting 3, 6, 12, 24,... From the former is equal to the latter
And 3,6,12,24,... Are equal ratio sequences with common ratio 2