Limit question

1. Sep 26, 2006

vabamyyr

I have a question:

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

2. Sep 26, 2006

arildno

"Do not opine, PROVE!"

Apocryphal quote from Euclid.

3. Sep 26, 2006

CRGreathouse

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

4. Sep 26, 2006

vabamyyr

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

5. Oct 1, 2006

manoochehr

manooch

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.

6. Oct 1, 2006

d_leet

It certainly does, it just isn't real.

7. Oct 2, 2006

8. Oct 2, 2006

manoochehr

thank you for help me

9. Oct 3, 2006

manoochehr

thank you for conduce:tongue:

Accordingly this sequence isn't convergent