Monday, 3 December 2012

limits - Is there a standard way to compute limlimitsntoinfty(fracn!nn)1/n?



I'm computing the radii of convergence for some complex power series. For one I need to compute
limn(n!nn)1/n.




I know the answer is 1e, so the radius is e. But how could you compute this by hand? I tried taking the logarithms and raising e by this logarithm, but it didn't lead me to the correct limit. (This is just practice, not homework.)


Answer



There are two formulas to compute radius of convergence of the series n=1cnzn
1R=limn|cn|1/n=limn|cn+1cn|.


Use the second one.


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