How can I do this troglodyte of a series

1. Dec 13, 2007

frasifrasi

The series, which is by all accounts nefarious, is (-1)^(n)*n*e^(-2^n).

In an attempt to subdue this monster, I made it into (-1)^(n)*n*/e^(2^n), but I do not want to wing the rest of the solution.

So, I ask for your help. Help me, brothers, like there is no tomorrow.

2. Dec 13, 2007

quasar987

Seems like a good candidate for Leibniz criterion of alternate series. If the general term in absolute value decrease and goes to zero, then the series converges.

3. Dec 13, 2007

DaveC426913

BTW, troglodyte simply means underground dweller.

4. Dec 13, 2007

frasifrasi

Thanks, but I need to know why it converges absolutely, which is the case...

5. Dec 13, 2007

quasar987

Can't you think of a convergence test you could apply on n*e^(-2^n) ?

6. Dec 14, 2007

frasifrasi

if tha absolute value converges...

n/e^(2n), I would assume e grows faster since it is an exponential function...so the abs value converges?

7. Dec 14, 2007

quasar987

That's an intuitive argument, not a mathematical proof.

(And the argument is flawed too. For instance, for the series of 1/n. We have that 1/n-->0, but the series of 1/n still diverges.)

Last edited: Dec 14, 2007
8. Dec 14, 2007

frasifrasi

Ok, so how else can I show that it is abs convergent? How should I demonstrate this?

9. Dec 15, 2007

quasar987

There is a plethora of citerion to determine the convergence of a series. Have you tried them all?

10. Dec 15, 2007