I would greatly appreciate it if I could get an explanation of how to solve this and not just the answers.

The real numbers a and b satisfy l a l<1 and l b l<1.

(a) In a grid that extends infinitely, the first row contains the numbers 1, a, a^2, a^3... The second row contains the numbers b, ab, a^2b... 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.

Link for grid #1: https://latex.artofproblemsolving.com/8/c/1/8c1cac67360acec4ef623054fed4ef33fd6c381a.png

(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.

Link for grid #2: https://latex.artofproblemsolving.com/e/3/9/e3959697cb9ff1295895297696a62834311cd76f.png

Guest Sep 12, 2020