Problema Solution

Calculate the sum of the following series.

0.27 + 0.0027 + 0.000027 + 0.00000027 + ...

Answer provided by our tutors

0.272727... = 0.27 + 0.0027 + 0.000027 + 0.00000027 + ...

= 0.27 + 0.27(.01) + 0.27(.01)^2 + 0.27(.01)^3 + ...

= 0.27 / (1-.01)

= 0.27 / 0.99

= 27/99

= 3/11