Question

series questions

Answer 1

@amistre64

Answer 2

the integral test is pretty much change n to x and integrate

Answer 3

n^4/n^6, since the bottom is bigger degree than top, the sequence an goes to zero

Answer 4

cant say i know what tests to choose tho :/

Answer 5

so 5 converges right and what is the test you used?

Answer 6

5 converges and the limit of an IS 0, but yeah, i got no solid on the tests used.

Answer 7

do you know anyone who can help me with this? I really dont know how to do this.

Answer 8

the next one, a test cant converge and diverge at the same time; and a test will either be converge, diverge, or inconclusive

Answer 9

I just tried that and its wrong.

Answer 10

which one you try?

Answer 11

number 6

Answer 12

yeah, which option?

Answer 13

2nd option

Answer 14

why?

Answer 15

i said: a test cant converge and diverge at the same time; and a test will either be converge, diverge, or inconclusive

Answer 16

you said the series converges and diverges at the saem time right

Answer 17

oh sorry I read that wrong

Answer 18

so which option is it?

Answer 19

it can be more than one

Answer 20

a little self reflection here. ive given ample hints for it :)

Answer 21

you said it can either converge diverge or be inconclusive. However I dont think the first option is right since comparision test doesnt take precedence so is it option 4

Answer 22

option 4 is what im thinking, the analysis is in errorsince one test says converge, the other says diverge

Answer 23

3 may be plausible, but i dont think its the most accurate

Answer 24

it may be possible to determine if the analysis is done correctly

Answer 25

4 is correct.

Answer 26

yay!! :)

Answer 27

do you know how to get the associated function for 3?

Answer 28

i believe, like i posted, change n to x

Answer 29

do I need to add +C to the answer?

Answer 30

no, its asking for the function that gets integrated, not for the integration itself

Answer 31

\[\sum f(n)\to\int f(x)\]

Answer 32

I did that and I got it wrong I got 1/2tan^-1(x)^2

Answer 33

f(x) is more compact; if it converges then the f(n) would have to converge as well

Answer 34

\[\frac{tan^{-1}(x)}{x^2+1}\]

Answer 35

yeah I took the indefinite integral of that

Answer 36

it doesnt ask you to do that

Answer 37

what does it ask then?

Answer 38

it asks what function of x you would use to integrate ....

Answer 39

Ok I understand now.

Answer 40

for example:\[\sum n^2\to\int x^2~dx\]
f(n) = n^2; f(x) = x^2

Answer 41

ok here is another problem I dont get

Answer 42

id suggest doing a root test on it

Answer 43

it converges

Answer 44

lim |n^(2/n) pi/4 |

Answer 45

the limit is about 3/4 right?

Answer 46

no its 0

Answer 47

http://www.wolframalpha.com/input/?i=limit+n%5E%282%2Fn%29+pi%2F4%2C+n+to+inf

Answer 48

it helps to actually take the root test

Answer 49

and the next one, i dont htink factorials are well suited to root tests