- #1

emnethesemn

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Hi and sorry if I misplaced the thread.

I'm having quite some trouble with analyzing the convergence of the following series :

Determine whether the series is convergent or divergent, absolutely & normally.

[tex]\sum[/tex]

I had troubles both with absolute and normal convergence.

With normal convergence

I tried Leibniz

1)

lim a(n) = 0 Which is ok {

(1+1/n)^n rises to

2)

a(n)=<v>=a(n+1)

I get to a part in which I have

and get them to equalize. So I guess normal convergence is fine. But I'm not sure of this.

When testing absolute convergence I figured out that I could state that it's smaller then

[tex]\sum[/tex]

but these series diverge so I'm nowhere.

I tried integral test but an integral of

I need to prove it Diverges absolutely, any ideas?

Sorry for all the bad grammar and anything that I left unclear, it's 2:00 am now /yawn and I just couldn't get LATEX to work, any guides on that matter would be appreciated as well.

Thanks in advance.

I'm having quite some trouble with analyzing the convergence of the following series :

## Homework Statement

:[/B]Determine whether the series is convergent or divergent, absolutely & normally.

[tex]\sum[/tex]

**(-1)^n * [e-(1+1/n)^n]**## Homework Equations

## The Attempt at a Solution

I had troubles both with absolute and normal convergence.

With normal convergence

I tried Leibniz

1)

lim a(n) = 0 Which is ok {

**lim e-(1+1/n)^n = 0**} as(1+1/n)^n rises to

**e**when we let**n**go to infinity.2)

a(n)=<v>=a(n+1)

I get to a part in which I have

**[1+1/n]/[1+1/(n+1)]<=1**I put limes on both sidesand get them to equalize. So I guess normal convergence is fine. But I'm not sure of this.

When testing absolute convergence I figured out that I could state that it's smaller then

[tex]\sum[/tex]

**|e|+|(1+1/n)^n|**but these series diverge so I'm nowhere.

I tried integral test but an integral of

**[(1+1/n)^n]dn**with range of**0 to +infinity**doesn't seem solvable.I need to prove it Diverges absolutely, any ideas?

Sorry for all the bad grammar and anything that I left unclear, it's 2:00 am now /yawn and I just couldn't get LATEX to work, any guides on that matter would be appreciated as well.

Thanks in advance.

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