How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n+1))/(n^1.5)# from #[1,oo)#?
is absolutely convergent
Given the series:
we can test for convergence the series:
#sum_(n=1)^oo abs((-1)^(n+1)/n^(3/2)) = sum_(n=1)^oo1/n^(3/2)#
If this series converges, then the series (1) converges absolutely ( and also conditionally ).
We can apply the integral test to the series (2) using the function:
Se we calculate:
which means that the series (1) is absolutely convergent.