GRE Subject Test: Math : Order of Convergence

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

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Example Questions

Example Question #1 : Numerical Approximation

For which values of p is 



Possible Answers:

All positive values of 


it doesn't converge for any values of 

Correct answer:



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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