Question

Sequences~

Answer 1

Determine whether \(\Large a_{n}={\frac{3+5n^2}{n+n^2}}\) diverges or converges. Also determine the sequence's tendency and find it's bounds

Answer 2

@ganeshie8 ?

Answer 3

@iambatman @ikram002p

Answer 4

@thomaster

Answer 5

@ParthKohli

Answer 6

so what test did u try ?

Answer 7

@Ashleyisakitty

Answer 8

I have had no practice in this area so sorry if Idk what you're talking about.. but I did the divergence test.

Answer 9

do u think its diverge or converge ?
(are you familier with comparasion test or ratio test ?)

Answer 10

this is just a sequence right ? @ikram002p

Answer 11

yes mm so ?

Answer 12

It diverges since the limit was not 0..

And I know the ratio test

Answer 13

looks we're mixing sequence and series

Answer 14

ohhh , ok i got ur point
but i was thinking if the series was converge then the seqence is converge as well

Answer 15

but finding the limit as a_n goes to infinity would be better , sry my bad lol

Answer 16

yes !

Answer 17

So based on the sequence test.. since it doesn't go to \(\infty\) it converges?

Answer 18

yes \(\large \lim \limits_{n\to \infty }a_{n}=\lim \limits_{n\to \infty }{\dfrac{3+5n^2}{n+n^2}} = \dfrac{5}{1}\)

Answer 19

since the limit exists, the sequence converges.

Answer 20

How would I find it's tendencies and bounds?

Answer 21

\[\large A \le \dfrac{3+5n^2}{n+n^2} \le B\]

Answer 22

I'm also not sure what they mean by `tendencies`, but we can try finding the bounds ^ @ikram002p help

Answer 23

we already have the upper bound
\[\large A \le \dfrac{3+5n^2}{n+n^2} \lt 5\]

Answer 24

@dan815

Answer 25

Luigi what does it mean tendency?

Answer 26

tendencies is the limit when n goes to infinity
bounded for sure 0<a_n<=5
mmm u can found another lower bound

Answer 27

the mean of the sequence?

Answer 28

oh ok

Answer 29

@ganeshie8 so what do you think ? n should be integer right ?
no need to minimize since its monotone
\(a_1=4\)
and upper bound 5

Answer 30

so
4<=a_n<5
right ?

Answer 31

yes its a monotone sequence for n > 3

check a_2 once

Answer 32

3.8