Answer:
Option B
Explanation:
Let ,
Sn= 9+99+999+.........n terms
$\Rightarrow$ $ S_{n}=(10-1)+(100-1)+(1000-1)+$.... n terms
$\Rightarrow$ $ S_{n}=(10+10^{2}+10^{3}+....... $ n terms -(1+1+..... n terms)
$\Rightarrow $ $S_{n}=\frac{10(10^{n}-1)}{10-1}-n$
$[a+ar+ar^{2}+..... ar^{n-1}= \frac{a(r^{n}-1}{r-1}, r>1]$
$\Rightarrow $ $S_{n}= \frac{10}{9}(10^{n}-1)-n$
put n=10
$\Rightarrow $ $S_{10}= \frac{10}{9}(10^{10}-1)-10$
$= \frac{10}{9}(10^{10}-1-9)$
$= \frac{10}{9}(10^{10}-10)=\frac{100}{9}(10^{9}-1)$
