Pascal Triangle

It is a geometric progression with a common ratio $r=2$ . The $n^{th}$ term of a geometric progression is given by $a_n=a_1 r^{n-1}$ . Substituting, we get

$a_{100}=1(2)^{99}=\boxed{2^{99}}$

We observe the pattern of the sum in the first few rows.

The pattern is $1,2,4,8,16,\cdots$

Therefore, we conclude that the $n$ th term of this series or the sum of numbers in $n$ th row is given by $2^{n-1}$ .

Therefore, sum of numbers in $100$ th row will be $\boxed{2^{99}}$