Remove one add one

The left column can be represented as :

$(1)[9(10^8)]+(2)[8(10^7)]+(3)[7(10^6)] + \dots + (8)[2(10^1)] + (9)[1(10^0)] \\ \Large =\displaystyle\sum_{n=1}^9 n(10-n)(10^{n-1})$

The right column can be represented as:

$(9)[1(10^8)]+(8)[2(10^7)]+(7)[3(10^6)] + \dots + (2)[8(10^1)] + (1)[9(10^0)] \\ \Large =\displaystyle\sum_{n=1}^9 (10-n)(n)(10^{n-1})$

This clearly proves that the given expression is $\Large\boxed{0}$ .

Consider the positive part on one side and negative part on other side. So for the unit's place, considering there are 9 1's at the left and 1 9 at the right, it leads to =9x1 - 1x9=0 For ten's place, there are 8 2's at the left and 2 8's at the right, it leads to= 8x2 - 2x8=0 Similarly for hundred's place, 7x3 -3x7=0 We keep on doing this and at the end, we get the result as 0.

when you get this type of problem that is in series always remember ans will be 1or 0

The last digit is 1 by substraction with 1 the final solution is 0;hence the problem is solved