Question

Use the integral test to determine whether the series below converges or diverges.

Answer 1

\[\sum_{n=1}^{\infty}\frac{ n }{ n^2+9 }\]

Answer 2

That means that you just compute the integral, with the same bounds.
Can you setup this integral?

Answer 3

i will be quite, but you sure as heck don't need no integral test for this
use the eyeball test

Answer 4

well the book wants me to use the integral test but not sure how to do it

Answer 5

replace the sum by an integral, using the bounds 1 and infinity

Answer 6

and replace the \(n\) by an \(x\)

Answer 7

the integral diverges so that means what?

Answer 8

so does the sum

Answer 9

but you knew that already, because the degree of the denominator is only one more than the degree of the numerator

Answer 10

I know how to set up the integral

Answer 11

i think it will be from 0 to infinty

Answer 12

because the degree differs by only 1, it will not converge

Answer 13

oh yeah that's true, so whats the point of using the integral test?

Answer 14

@mido really makes no difference, what happens at the beginning is irrelevant

Answer 15

@Ldaniel not everything is a rational function
the integral test is useful when it is less obvious

Answer 16

try

Answer 17

i mean when the convergence or divergence is less obvious

Answer 18

What does the integral test yield? .. infinity?

Answer 19

in this case yes, because the sum diverges

Answer 20

are u set up it

Answer 21

so the series diverge ?

Answer 22

i think this