Limit of (2.3, 2.33, 2.333, )

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SUMMARY

The limit of the sequence (2.3, 2.33, 2.333, 2.3333, ...) converges to 2.333..., which can be expressed as the fraction 7/3. The discussion emphasizes that the limit exists and is derived from the understanding of repeating decimals as rational numbers. Additionally, it highlights that the limit of a related sequence (0.3, 0.33, 0.333, 0.3333, ...) is 1/3, contributing to the overall limit of the original sequence.

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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?
 
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PirateFan308 said:

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.
 
Remember that a repeating decimal represents a rational number. You should be able to express it as a fraction.
 
Wow, that is so simple. Thank you!
 
PirateFan308 said:
Wow, that is so simple. Thank you!

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

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