Question

I am a little confused how to find the behavior of the alternating series of this function?

Answer 1

\[\sum_{1}^{\infty}[(-1)^n(1/\sqrt{n})\]

Answer 2

I understand that \[a_{n} = 1/\sqrt{n}\]

But it says that \[0 <a_{n}+1<a_n\]

I am a little confused in how to implement this process and method to find behavior of the alternating series.

Answer 3

second part just says the terms are positive and decreasing, which they are since \[\frac{1}{\sqrt{n+1}}<\frac{1}{\sqrt{n}}\]

Answer 4

terms are decreasing and going to zero, that is enough for the alternating series test

Answer 5

btw it is \[0<a_{n+1}<a_n\] i think

Answer 6

Yah you are right, I miss wrote it...

I am a little confused in how the second part shows decreasing?

Answer 7

since \(n+1>n\) then \(\sqrt{n+1}>\sqrt{n}\) and so \[\frac{1}{\sqrt{n+1}}<\frac{1}{\sqrt{n}}\] it is more or less obvious if you think about it

Answer 8

ohhh, I see!
This is simple I am just confusing myself.
Thanks!

Answer 9

yw