GRE Subject Test: Math : Comparing Rates of Convergence

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

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Example Questions

Example Question #651 : Gre Subject Test: Math

For which values of p is 

 

convergent?

Possible Answers:

only 

All positive values of 

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

.

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