+101 Compute the sum as a common fraction: 1.11111111…0.11111111…0.01111111…0.00111111…0.00011111…0.00001111…0.00000111…+⋮ ?
+130466 This is an infinite geometric sum and can be expressed as
1 + (1/9) + (1/9) + (1/90) + (1/900) + ......... =
(10/9) + (1/9) + (1/90) + (1/900) + .........
The first term is (10/9) and the common ratio = (1/10)
So......the infinite sum is
(10/9) (10/9)
_________ = ________ = (10/9) * (10/9) = 100 / 81
1 - (1/10) (9/10)
