- #1
Caiti
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Homework Statement
I've been given a question that makes use of 5^(n)*sin(pi*n!)
The question merely asks if the sequence converges, and if so, to determine its limit. Am I right in assuming that this does converge, under the definition, but does so as n-> - infinity?
So basically, I believe this diverges for n-> infinity. However, for n-> - infinity I believe it will converge to 0. Using the definition of convergence, am I allowed to stay it converges?
Homework Equations
The definition of convergence:
A sequence converges as n-> infinity if there is an n>N given any E>0 where |U_n - L| < E
or
U_n -> L as n-> infinity
The Attempt at a Solution
The above definition actually changes my mind. It seems to only states that a sequence is converging if it meets conditions and n-> infinity, and so n-> - infinity wouldn't fit the definition. The question definitely doesn't specify what n is tending to, so my question is literally just whether this is classed as convergence or not?
Thank you very much