Question

Does \(x_n = \dfrac{(-1)^n n}{n+1}\) converge or diverge?
Please, help

Answer 1

If we take \(lim x_2n\) and \(lim~ x_{2n+1}\) we can see that it is divergent. However, if I Use definition of lim , I see it converge to 1. What's wrong?

Answer 2

@phi

Answer 3

its divergent :O

Answer 4

i saw what u wrote using 2n , 2n+1
which is correct , so whats wrong ?

Answer 5

i agree with @ikram002p

Answer 6

if you use definition of lim, you can see that it converges

Answer 7

how ?

Answer 8

to use defenition u need to split this series into two series :O

Answer 9

Let me show:
by definition, let \(\varepsilon \)>0 , let n > N = 1/\(\varepsilon\)

Answer 10

yes @khurramshahzad

Answer 11

mere msg nhi mila kia ?

Answer 12

\(\forall n>N\)\(\dfrac{1}{n}<\dfrac[1}{N}\)
You guys, Please don't mess up my post

Answer 13

nahi mila.

Answer 14

network problem bahut hai.

Answer 15

Please, be polite.

Answer 16

yup just os ka msla hy

Answer 17

shereeen

Answer 18

@Loser66 u can post ur question here ,OS seems to be laging
http://math.stackexchange.com/questions/ask

Answer 19

Ok, I am gonna close the post. You think OS is wrong, but I don't think so, the wrongness come from people who are impolite.

Answer 20

I will see you later. Thanks girl

Answer 21

plz at least continue what u were writing xD
its div why ?
cuz even the limit def u should covert the sequence into two other sequences
i wanted to seehow did u do it :O

Answer 22

and sorry OS keeps laging xD

Answer 23

I'll scan my stuff. :)

Answer 24

@ikram002p

Answer 25

hmm u only worked on the even part , u should do the limit def again assuming n is odd , so u would have -1 limit
which gives u not unique limit ,hence it does not converge.

Answer 26

Ok, got the part I am missing. Thank you, girl

Answer 27

:)

Answer 28

hahaha.... yes, we did.

Answer 29

;)