Consider $T$ = $9 \times 99 \times 999 \times 9999 \times \cdots \times \underbrace{999....9}_{2015 \:nines}$
Find the last 3 digits of $T$
Advise: I wrote it down wrong the first time, it should be a product of "2015" numbers, i apologize about that, i realized my fault when i was travelling and i couldn't repare it in my cellphone.
My try
I know the last digit, i found it easily, but the struggle is with the others. I tried this:
$9 \times 99 \times 999 \times \cdots \times \underbrace{999 \ldots 9}_{2015 \:nines}$ $= 9 \times 9(11) \times 9(111) \times \cdots \times 9(\underbrace{111 \ldots 1}_{2015 \:ones})$
So $T$ = $9(1+11+111+ \cdots +\underbrace{111 \ldots 1}_{2015 \:ones})$
But from here i found nothing, any hints?
9*99*999*999
and get the last 3 digits of the result? $\endgroup$ – Cristian Lupascu Feb 6 '18 at 13:10