Limit of (2.3, 2.33, 2.333, )

[PirateFan308]

Homework Statement

Compute the limit of the following sequences (show work):
(2.3, 2.33, 2.333, 2.3333, ...)

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?

 

[Mark44]

Homework Statement

Compute the limit of the following sequences (show work):
(2.3, 2.33, 2.333, 2.3333, ...)

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?

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.

 

[LCKurtz]

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

 

[PirateFan308]

Wow, that is so simple. Thank you!

 

[LCKurtz]

Wow, that is so simple. Thank you!

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