Limit of (2.3, 2.33, 2.333, )

  • #1

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?
 

Answers and Replies

  • #2
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6,394

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.
 
  • #3
LCKurtz
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Remember that a repeating decimal represents a rational number. You should be able to express it as a fraction.
 
  • #4
Wow, that is so simple. Thank you!
 
  • #5
LCKurtz
Science Advisor
Homework Helper
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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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