Question

Please say, to what limits will the following series tend as the number of terms increases indefinitely:
(a) 0.1+0.001+0.000 01+...........
(b) 0.06+0.0006+0.000 006+.........
(c) 0.16+0.0016+0.000 016+..........
What is the connection between these series?

Answer 1

All of these are getting smaller...and smaller... and smaller.
0 being the "smallest number" available, I'd say they are tending towards that :)

Answer 2

The answer is:
(a) 10/99; (b) 6/99; (c) 16/99
The series (c) is the sum of (a) and (b). It represents 0.161 616......., a recurring decimal.