Question 82383
0.21+0.0021+0.000021+...
This is a repeating decimal so it is a rational number. 
-----------
Adding the terms you would get 0.2121212121....
Let x= 0.212121212...
Then 100x = 21.2121212121...
Subtract the 1st equation from the 2nd to ge:
99x= 21
Then x=21/99
===========================
Cheers,
Stan H.