Series question

1. Feb 4, 2008

nuclearrape66

does the series from 1 to infinity of $$\sum$$(1 - (2/n))^3n convegre or diverge.

i've tried almost all the tests and cant figure it out....

2. Feb 4, 2008

3. Feb 4, 2008

quasar987

Have you even tried the simplest test of them all? Does the argument of the series goes to 0 as n increases without bounds?

4. Feb 4, 2008

nuclearrape66

i've tried the root test. does not work. meaning it's inconclusive.

and i dont understand your question.
"Does the argument of the series goes to 0 as n increases without bounds?"
are you saying do the terms get closer to zero? yes.

5. Feb 4, 2008

nuclearrape66

if you can hint me to what test i should use maybe i can figure it out.

6. Feb 5, 2008

quasar987

Yes, this is what I was asking, but 'yes' is not the answer I had in mind!

Remember that

$$\left(1+\frac{1}{n}\right)^n \rightarrow e$$

!

7. Feb 5, 2008

nuclearrape66

and therefore by the divergence test...the series diverges?

8. Feb 5, 2008

quasar987

I was merely pointing out a sequence that behaves like the argument of your series and that does not go to 0.

However, you can cleverly manipulate the identity

$$\left(1+\frac{1}{n}\right)^n \rightarrow e$$

to find the precise value of the limit you're interested in.