, 
converges absolutely if
.Calculus
Lesson
53
Ratio
and Root Tests
Back to Dr. Nandor's Calculus Notes Page
Back to Dr. Nandor's Calculus Page
These are the last 2!
Ratio Test:
if all , converges absolutely if
.
Test fails if 
diverges if 
Root Test:
if all 
, 
converges absolutely if
Test fails if 
.
diverges if 
.
Examples:
Methods:
1) Test nth term - if not zero, the series diverges.
2) Is it geometric, p-series, telescoping, or alternating? If so, write down test result.
3) Can integral, root, or ratio test be applied? If so, test! If test fails or if you can't
tell, try another one!
4) Can the series be compared to another?
More Examples:
