Find Limit of Sequence: 6/7 or Divergent?

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Homework Help Overview

The discussion revolves around finding the limit of a sequence defined by a_n=(5-9n+6n^4)/(7n^4+5n^3-3) and determining whether it converges or diverges.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to evaluate the limit and expresses confusion regarding the relationship between the limit and divergence, questioning if a non-zero limit indicates divergence.

Discussion Status

Some participants have pointed out a potential misunderstanding between sequences and series, which has led to a clarification of the original poster's thought process. The conversation is exploring the implications of this distinction.

Contextual Notes

The original poster's confusion stems from a possible mix-up between the concepts of sequences and series, which is being addressed in the discussion.

iceman_ch
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Homework Statement



Find the limit of sequence if it converges; otherwise indicate divergence.

a_n=(5-9n+6n^4)/(7n^4+5n^3-3)

answers

a=6/7
b=-2
c=5/7
d=diverges

Homework Equations



none

The Attempt at a Solution



The limit of A_n is equal to 6/7 which is one of the answers but, I thought that if the limit doesn't equal zero then it is divergent? Any help would be great.

Thanks
 
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You may be confusing sequences with series. You question involves sequences
 
Well now I feel stupid. I can't believe I missed that. For some reason I thought it was saying series. Thanks for pointing that out.
 
:smile: yeah, the trickiest questions are the one where we don't dare to spot the obvious. I can't count how many times this happens to me with math problems.
 

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