GRE Subject Test: Math : Comparing Rates of Convergence

Example Questions

Example Question #1 : Comparing Rates Of Convergence

For which values of p is

convergent?

All positive values of

only

it doesn't converge for any values of

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

.