# Limit of (2.3, 2.33, 2.333, )

1. Nov 2, 2011

### PirateFan308

1. The problem statement, all variables and given/known data
Compute the limit of the following sequences (show work):
(2.3, 2.33, 2.333, 2.3333, ...)

3. The attempt at a solution
Theoretically it approaches 2.333... but I don't think this is the correct answer (and I am not sure how to show it). Does the limit not exist?

2. Nov 2, 2011

### Staff: Mentor

If the sequence happened to be (0.3, 0.33, 0.333, 0.3333, ...), what would the limit of the sequence be? The limit of your sequence is 2 plus the limit of this sequence.

3. Nov 2, 2011

### LCKurtz

Remember that a repeating decimal represents a rational number. You should be able to express it as a fraction.

4. Nov 2, 2011

### PirateFan308

Wow, that is so simple. Thank you!

5. Nov 2, 2011

### LCKurtz

How "simple" it is depends on how detailed the "show your work" is supposed to be.