• Support PF! Buy your school textbooks, materials and every day products Here!

Using root test and ratio test for divergence

  • Thread starter superdave
  • Start date
  • #1
150
3

Homework Statement



Does this series converge or diverge?

Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1)



Homework Equations





The Attempt at a Solution



Okay, I've tried it both ways.

Ratio test:

lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1))

Now, that doesn't appear to simplify in anyway that would make using l'hospital's rule possible to find the limit.

Root test:

lim n --> inf. of -3*n^(1/n) / 4^((n-1)/n)

That bottom part throws me off.
 

Answers and Replies

  • #2
1,074
1
Why does it through you off? What is the limit of (n-1)/n as n goes to infinity?
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,808
933

Homework Statement



Does this series converge or diverge?

Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1)



Homework Equations





The Attempt at a Solution



Okay, I've tried it both ways.

Ratio test:

lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1))

Now, that doesn't appear to simplify in anyway that would make using l'hospital's rule possible to find the limit.
Seriously? You are aware, are you not, that (-3)^(n+1)/(-3)^n= -3? The (4^n part is just as easy! You should not need L'Hospital's rule.

Root test:

lim n --> inf. of -3*n^(1/n) / 4^((n-1)/n)

That bottom part throws me off.
 

Related Threads on Using root test and ratio test for divergence

  • Last Post
Replies
1
Views
948
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
885
Replies
2
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
2
Views
812
Replies
2
Views
2K
  • Last Post
Replies
10
Views
1K
Replies
1
Views
2K
Top