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Why does Mathematica provide incosistent convergence conditions?

Posted 10 years ago
In[1]:= Clear[a, n]
In[2]:= SumConvergence[(n^(n - 2))/((a^n)*(n!)), n]
Out[2]= Abs[a] > E
In[3]:= SumConvergence[(n^(n - 2))/((E^n)*(n!)), n]
Out[3]= True

All right. So, according to Out[2], the series is convergent if and only if the absolute value of variable a is greater then the constant e. But, according to Out[3], the series is convergent if a=e! Since Abs[e] is not greater then e, this output seems incosistent to me... Where lies the problem?

POSTED BY: Marcin Ga??zka
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