How do you apply the ratio test to determine if Sigma 1/n^3 from n=[1,oo) is convergent to divergent?
1 Answer
Mar 21, 2018
It's convergent. You may use the integral test to prove this.
Explanation:
The ratio test isn't the correct test. I would use the integral test.
We need to evaluate the integral
=int_1^oo 1/n^3 dn
=lim_(t-> oo) int _1^t 1/n^3 dn
=lim_(t-> oo) [-1/2n^-2]_1^t
=lim_(t->oo) -1/2t^-2 - (-1/2(1)^-2)
=0 + 1/2
= 1/2
Since
Hopefully this helps!