Infinite series (damn mickey mouse)

kring_c14
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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??
 
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because .27 + .0027 + .000027 = .272727
.27 + .027 = .297 -> .297 +.0027 = .2997 etc
 
ahhh..haven't thought of it...thanks
 

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