All GRE Subject Test: Math Resources
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
.
All GRE Subject Test: Math Resources
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