Calc question..

Question

Use geometric series to find the rational number represented by the decimal: Vinculum above number of (.48) . r =

1. .01
2. .1
3. 48
4. .48

Answer 1

a + ar + ar² + ar³ + … = .‾‾‾₄₈ with the line on top, call it x₄₈^; then we can rewrite x₄₈ as 0.48 + 0.0048 + 0.000048 + … which in our a-r geometric series form is .48 + .48(1/100) + .48(1/100)² + .48(1/100)^{3 = ... . SO IT LOOKS LIKE (1/100) TAKES THE PLACE OF r in the geometric series.}

^{Ans: .01}