- #1
penroseandpaper
- 21
- 0
- Homework Statement
- Convergent
- Relevant Equations
- Convergent and divergent
A sequence is made up of two sequences
an=(n^2)/(n+2) - (n^2)/(n+3)
The problem asks for the solver to work out if it's converging or diverging, and find a limit if possible.
My first thought was to write both over a common denominator and then divide through by the dominant term; this implied converging with a limit of 1 for the positive values of n.
But if the reciprocal rule is instead applied, both are null sequences which therefore tend to infinity.
It's obviously divergent, so I guess the lesson is don't mess with the original question?
Thank you
[Moderator's note: Moved from a technical forum and thus no template.]
an=(n^2)/(n+2) - (n^2)/(n+3)
The problem asks for the solver to work out if it's converging or diverging, and find a limit if possible.
My first thought was to write both over a common denominator and then divide through by the dominant term; this implied converging with a limit of 1 for the positive values of n.
But if the reciprocal rule is instead applied, both are null sequences which therefore tend to infinity.
It's obviously divergent, so I guess the lesson is don't mess with the original question?
Thank you
[Moderator's note: Moved from a technical forum and thus no template.]
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