1 + 0 * 9 = 1,2 + 1 * 9 = 11,3 + 12 * 9 = 111 until 9 + 123456789 * 9 = 111111111 is there any rule

1 + 0 * 9 = 1,2 + 1 * 9 = 11,3 + 12 * 9 = 111 until 9 + 123456789 * 9 = 111111111 is there any rule

According to your previous rule, the last one should be 9 + 12345678x9 = 111111111, which is characterized by the fact that the number on the left side of the plus sign is 1.5 times larger than the single digit of the multiplier on the right side of the plus sign
In these equations, the left side can be expressed as
n+(1x10^(n-2)+2x10^(n-3)+… +(n-2) X10 + (n-1)) x9,2 ≤ n ≤ 9, then
n+(1x10^(n-2)+2x10^(n-3)+… +(n-2)x10+(n-1))x9
=n+(1x10^(n-2)+2x10^(n-3)+… +(n-2)x10+(n-1))x(10-1)
=n+1x10^(n-1)+2x10^(n-2)+… +(n-2)x10^2+(n-1)x10-(1x10^(n-2)+2x10^(n-3)+… +(n-2)x10+(n-1))
=1x10^(n-1)+2x10^(n-2)+… +(n-2)x10^2+(n-1)x10+n
-1x10^(n-2)–… –(n-3)x10^2–(n-2)x10–(n-1)
=1x10^(n-1)+1x10^(n-2)+… +1x10 ^ 2 + 1x10 + 1 (i.e. n ones)
Take 9 + 12345678x9 = 11111111 as an example
9+12345678x9=9+12345678x(10-1)
=9+123456780-12345678
=123456789-12345678
=111111111
It should be noted that equation 1 + 0x9 = 1 does not belong to this law