# 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.