GRE Subject Test: Math : Order of Convergence

Study concepts, example questions & explanations for GRE Subject Test: Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #11 : Comparing Series

For which values of p is 

 

convergent?

Possible Answers:

All positive values of 

only 

it doesn't converge for any values of 

Correct answer:

only 

Explanation:

We can solve this problem quite simply with the integral test. We know that if 

converges, then our series converges. 

We can rewrite the integral as 

and then use our formula for the antiderivative of power functions to get that the integral equals

.

We know that this only goes to zero if . Subtracting p from both sides, we get

.

Learning Tools by Varsity Tutors