# 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