To find the sum of the sequence $1,10,100,1000,\dots ,1,000,000,000$, we note that it is a geometric sequence where:

- The first term $a=1$
- The common ratio $r=10$
- The last term $l=1,000,000,000$

First, determine the number of terms in the sequence.

The general term of the geometric sequence can be written as:

$$a_n=a\cdot r^{(n-1)}$$

Set $a_n=1,000,000,000$:

$$1,000,000,000=1\cdot {10}^{(n-1)}$$

$${10}^{(n-1)}=1,000,000,000$$

Since $1,000,000,000={10}^9$, we have:

$$n-1=9$$

$$n=10$$

So there are 10 terms in the sequence.

The sum $S_n$ of the first $n$ terms of a geometric sequence is given by:

$$S_n=a\frac{r^n-1}{r-1}$$

Substituting the known values:

- $a=1$
- $r=10$
- $n=10$

$$S_{10}=1\frac{{10}^{10}-1}{10-1}$$

$$S_{10}=\frac{{10}^{10}-1}{9}$$

Calculate ${10}^{10}-1$:

$${10}^{10}=10,000,000,000$$

$${10}^{10}-1=9,999,999,999$$

Now, divide by 9:

$$\frac{9,999,999,999}{9}=1,111,111,111$$

Thus, the sum of the sequence is:

A. 11,111,111,111