Help. Thanks!

The real numbers $a$ and $b$ satisfy $|a| < 1$ and $|b| < 1.$

(a) In a grid that extends infinitely, the first row contains the numbers $1, a, a^2, \dots.$  The second row contains the numbers $b, ab, a^2b, \dots$    In general, each number is multiplied by $a$ to give the number to the right of it, and each number is multiplied by $b$ to give the number below it.

Find the sum of all numbers in the grid.
 

(b) Now suppose the grid is colored like a chessboard, with alternating black and white squares, as shown below. Find the sum of all the numbers that lie on the black squares.

Thank you!

-NerdWallet