Multiplication By Patterns

Note that every 99999....9999 can be expressed in the form $10^n-1$ for some integer $n>1$ . Let's see what happens when we square it:

$(10^n-1)^2 = 10^{2n} - 2\times 10^n + 1 = 10^n(10^n-2)+1$

Hence the general pattern for $n$ number of 9's is given by $10^n(10^n-2)+1$ and for this question , put $n=5$ :)

I just read on patterns generated from 99 *2 . Each samples of Numbers given have increased as one digit number at a time There're, nimbers will be added by one number each sections of 9 and 0 from 99980001to providing an answer is 9999800001 . Sorry mine is not logical one at all.