Question

test the series for convergence or divergence

Answer 1

?

Answer 2

Isn't Divergent a movie ??

Answer 3

\[\sum_{n=0}^{\infty}\frac{ (-1)^{n-1} }{ \ln(n+4) }\]

Answer 4

AST

Answer 5

AST?

Answer 6

you ast the question right?

Answer 7

Alternating series test, from what it looks like

Answer 8

But how do I do that?

Answer 9

If\[b_{n+1} \le b_n\]and \[\lim_{n \rightarrow \infty} b_n =0\] you should have a convergent series

Answer 10

\[b_n = \frac{ 1 }{ \ln(n+4) }\] I believe

Answer 11

So what that really means is, you have to show \[b_n\] is decreasing and then there's the limit definition as above

Answer 12

in english, the absolute value of the terms go to zero, and the series alternates (because of the \((-1)^n\)

Answer 13

And by decreasing I mean, taking the derivative \[f(x) = \frac{ 1 }{ \ln(x+4) }\]

Answer 14

so it would be convergence

Answer 15

Correct

Answer 16

thanks