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October 5th, 2013, 09:39 AM   #1
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Limit calculating methods

Hi guys
I want to collect the methods of calculating limit of the sequences.
1.dividing with n on the highest degree(works only with fractions if i'm right) then using the remarkable limits(this is basically used at the end of almost all method)
2.using remarkable identities
3.factorization
4.estimation then using that if an-->a and cn-->a and an<=bn<=cn then bn-->a(i dont know how we call this)
5.using the definition of limit,guessing the limit then searching an n0 index number
i think this is all i know at the moment,
i know you need to use different method on different sequences,but its good to know what you can choose of
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October 7th, 2013, 09:02 AM   #2
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Re: Limit calculating methods

Quote:
Originally Posted by ricsi046
4.estimation then using that if an-->a and cn-->a and an<=bn<=cn then bn-->a(i dont know how we call this)
We can call the Squeeze theorem or Sandwitch theorem. In general it is easier to test for convergence rather than finding the limit. To find the limit we usually use the L'Hospitale rule, series expansion , Squeeze theorem ,algebraic manipulations or approximations.
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