Does the Limit of 1/(3+(-1)^n) Exist?

[vabamyyr]

I have a question:

what is lim (n--->infinity)= 1/(3+(-1)^n))? My opinion that this limit does not exist.

 

[arildno]

"Do not opine, PROVE!"



Apocryphal quote from Euclid.

 

[CRGreathouse]

Are you asking about
$$\lim_{n\rightarrow\infty}\frac{1}{3+(-1)^n}$$
perhaps? The equals sign in your post is confusing me. If so, are you familiar with the lim sup and lim inf? That would give you an easy direct proof: if lim sup = lim inf, that's the limit; otherwise, the limit does not exist.

 

[vabamyyr]

i have dealt with sup but not with inf but i will look them up. Thx anyway.

 

[manoochehr]

manooch

I have a question:

what is lim (n--->infinity)= 1/(3+(-1)^n))? My opinion that this limit does not exist.

if n∈Z (Z=Integer) then we have two answer for equation

1) if n=Even then answer=1/4

2) if n=Odd then answer=1/2

if n∈R (R=Real) then equation is undefined

for example: (-1)^1/2 does not exist.

 

[d_leet]

for example: (-1)^1/2 does not exist.

It certainly does, it just isn't real.

 

[Edgardo]

I think you could use:

Proposition 4 Every subsequence of a convergent sequence converges to the same limit.
from: http://www.iwu.edu/~lstout/sequences/node3.html

 

[manoochehr]

thank you for help me

 

[manoochehr]

thank you for conduce:tongue:

Accordingly this sequence isn't convergent