- #1

vabamyyr

- 66

- 0

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

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- Thread starter vabamyyr
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- #1

vabamyyr

- 66

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

- #2

arildno

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"Do not opine, PROVE!"

Apocryphal quote from Euclid.

Apocryphal quote from Euclid.

- #3

CRGreathouse

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[tex]\lim_{n\rightarrow\infty}\frac{1}{3+(-1)^n}[/tex]

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

vabamyyr

- 66

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

- #5

manoochehr

- 6

- 0

vabamyyr said:

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.

- #6

d_leet

- 1,077

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

It certainly does, it just isn't real.

- #7

Edgardo

- 705

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Proposition 4 Every subsequence of a convergent sequence converges to the same limit.

from: http://www.iwu.edu/~lstout/sequences/node3.html

- #8

manoochehr

- 6

- 0

thank you for help me

- #9

manoochehr

- 6

- 0

thank you for conduce:tongue:

Accordingly this sequence isn't convergent

Accordingly this sequence isn't convergent

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