How do you find the interval of convergence #Sigma ((-1)^n(x+2)^n)/n# from #n=[1,oo)#?
1 Answer
The series:
is absolutely convergent for
Explanation:
To find the interval of convergence we can apply the ratio test, stating that a necessary condition for a series
If
Let's calculate the ratio:
so that:
we can therefore conclude that the series is absolutely convergent for
In the case where
that is divergent, while for
that is convergent, but not absolutely convergent.
In conclusion the series converges for