# Limit question

vabamyyr
I have a question:

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

Homework Helper
Gold Member
Dearly Missed
"Do not opine, PROVE!"

Apocryphal quote from Euclid.

Homework Helper
$$\lim_{n\rightarrow\infty}\frac{1}{3+(-1)^n}$$
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

vabamyyr said:
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

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

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

d_leet
manoochehr said:
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