- #1

emnethesemn

- 4

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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 :

[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 1:40am and I just couldn't get LATEX to work, any guides on that matter would be appreciated as well.

Thanks in advance.

Just noticed, this is a self study and I guess I posted it in the wrong place as I assumed. My apologies.

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

[tex]\sum[/tex]

**(-1)^n * [e-(1+1/n)^n]**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 1:40am and I just couldn't get LATEX to work, any guides on that matter would be appreciated as well.

Thanks in advance.

Just noticed, this is a self study and I guess I posted it in the wrong place as I assumed. My apologies.

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