A Curious Pattern

In pascal's triangle, each number is the sum of the number to it's top left + top right. Every time you go down a layer, each number of the previous numbers is calculated twice, one time as the top left number and one time as the top right number. Therefore, the size doubles each time you go down a row. To find the 10th row (with the top being the 0th), simply find 2^10.

The sum of each row of the Pascal's Triangle is in the nth row is $2^n$ and n in this problem is 10 and so $\color{#20A900}{2^{10}}$ is $\color{#3D99F6}{1024}$