# Limit question

I have a question:

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

arildno
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Gold Member
Dearly Missed
"Do not opine, PROVE!"

Apocryphal quote from Euclid.

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

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

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.

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

It certainly does, it just isn't real.

thank you for help me

thank you for conduce:tongue:

Accordingly this sequence isn't convergent