The attachment has a typo. It should be:
The rest is correct. For example, starting with 1122 (n=2) you have:
I have a number theory problem with solution but i dont understand why one can write this equallity (green question mark). Because 1122 is not 11*22 or 111222 is not 111*222.
ImageShack® - Online Photo and Video Hosting
To me it looks like the expression immediately after the green question mark and before the next equal sign...
1/9(10^n -1).2/9(10^n -1)
i think that dot separates 1's and 2's
Examples: n = 1
1/9(9).2/9(9) = 1.2, '1 dot 2' or twelve
n = 2
1/9(99).2/9(99) = 11.22, '11 dot 22' or 1122
n = 3
1/9(999).2/9(999) = 111.222, '111 dot 222' or 111222
Am I stretching it too much?