How do you test for convergence of #Sigma n e^-n# from #n=[1,oo)#?
We can determine the convergence of the series:
using the ratio test:
As the limit is less than
so, as we can observe, the series is convergent for
The series is convergent by the ratio test.
Use the ratio test:
(Dividing is the same as multiplying by reciprocal of denominator)
Since the ratio test gives a value less than one, the series is convergent by the ratio test.