Alternative examples, alternating series test

[micromass]

So when dealing with these, should I avoid simplifying? because i got ∑-1/n but before simplification i got ∑1/n-(1/n+1/n)

Sure, but write it even differently. Write it so that the odd term is $1/n$ and the even term is $-2/n$.

 

[Abscissas]

OHHHHHHHHH I see what you did now ∑1/n-2/n which would diverge because to goes to 2 and your a genius haha thanks man

 

[Abscissas]

Idk why, but i was trying to make it converge

 

[Abscissas]

But wait, it would then violate the rule that it goes to 0, and i feel like I am wrong on this one, but its not alternating

 

[Abscissas]

Because each sum, is negative, or when we say its alternating do we just mean each term?

 

[Abscissas]

each term of the series*

 

[micromass]

It means the terms converge to zero.

 

[Abscissas]

So when i read this, I think of a wave dimming. Is this the right idea?

 

[micromass]

Uh, I don't know. I don't have that picture in my mind. But yours could be helfpul.

 

[Abscissas]

Okay, so here is my problem, I am working on 2(1/n)^n. The ^n is to make it alternate. the 1/n is to make it go to zero, and then the 2 is to make it not go to zero. How can something diverge, and still go to zero?

 

[Abscissas]

2(-1/n)^n, sorry about that