Question

easy question: For which of these series is the Integral Test not appropriate?

Answer 1

anyone?

Answer 2

freckles, please tell me youre going to take a stab at it!

Answer 3

i think its the last one, since that one seems impossible to integrate
i mean look at that thing, ugly as hell lol

Answer 4

Well do you know which of the thingys inside the summation signs is integratable ?

Answer 5

first one is a log, you could use the integral test for tha

Answer 6

you are right

Answer 7

that last one doesn't seem easy to integrate

Answer 8

but the ones before it are definitely are

Answer 9

i hate to disagree with my learned colleague @freckles but i think the last one is easy to integrate

Answer 10

well I did say seems

Answer 11

put \(u=\tan^{-1}(x)\) and you get it right away

Answer 12

I haven't attempt to integrate it

Answer 13

@freckles, right but it couldnt be that easy right? they probably WANT me to think that its not integratable just because it seems daunting

Answer 14

i think it might actually be the second one

Answer 15

i think the point is that finding the antiderivative of cosine doesn't help you any

Answer 16

there are actually conditions in which you can apply the integral test

Answer 17

@satellite73 ohhhh because it just gives a sin, right?

Answer 18

you just end up chasing your tail, since you go right to sine, and that is just as unclear as cosine
i think the questions isn't which ones you can integrate, but which one will not give you any new info

Answer 19

@satellite right right

Answer 20

sorry freckles, satellite's gonna have to get the medal on this one,

Answer 21

i just wanna thank @freckles and @satellite73, and anyone else on this thread,

Answer 22

and also f has to be decreasing, continuous, and positive on [1,inf)

Answer 23

this is my first day on openstudy, and man it really is great, very stimulating

Answer 24

and cos(xpi) isn't always positive

Answer 25

and its it always decreasing either

Answer 26

oh good point
kind of forgot about that

Answer 27

@freckles and @satellite73 , i just got the answers, the cos one was ...wait for it.. CORRECT!

Answer 28

wait @freckles, then how come it was the right answer? i dont get it. if cos isnt always positive

Answer 29

what?

Answer 30

I agreed that cos was the right answer
and I gave my real why
it doesn't satisfy the conditions of the integral test
which was that it needs to be continuous, positive, and decreasing

I said cos(pix) isn't always positive and isn't always decresaing

Answer 31

the conditions aren't met for the cos(pix)

Answer 32

reason (not real) lol

Answer 33

ohhhh right, whoops, forgot that the question was asking which should NOT use the integral test