[tex]\displaystyle\bf\\e=10^9-9\times10^8-9\times10^7-9\times10^6-....-9\times10-1\\\\e=10^9-9(10^8+10^7+10^6+...+10^1)-1\\\\e=10^9-9\times\left(\frac{10^{8+1}-1}{10-1}-1\right)-1\\\\\\e=10^9-9\times\left(\frac{10^{9}-1}{9}-1\right)-1\\\\\\e=10^9-9\times\frac{10^{9}-1}{9}-9-1\\\\e=10^9-(10^{9}-1)-9-1\\\\e=10^9-10^{9}+1-9-1\\\\\boxed{\bf e=-9}[/tex]
