Infinite series (damn mickey mouse)

[kring_c14]

Homework Statement

the repeating decimal . 27272727 . . . can be written as an infinite series. Write it as a series and tell if it diverges/converges. If it converges, find the sum.


Mickey, also a former student, knows how to do this one. Mickey knows enough math to write it as .27 + .0027 + .000027 . . .

It's now an infinite series. Mickey spots the common ratio of the series as .0027/.27 = .01. Therefore, it converges! He use the formula and presto:
S = .27/(1 - .01) = .27/.99 = 27/99 = 3/11
(remarkable achievement considering he's a mouse!)

The Attempt at a Solution

why did mickey wrote .0027 after .27?? why not .027??

 

[R*E*M]

because .27 + .0027 + .000027 = .272727
.27 + .027 = .297 -> .297 +.0027 = .2997 etc

 

[kring_c14]

ahhh..haven't thought of it...thanks