Where did the formula for summing finite geometric series come from? Suppose the geometric series has first term a₁ and constant ratio r , so that S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹

b. Use part (a) to show that S n -r S n = a₁ - a₁ rⁿ .