Question

Convergence of this series?

Answer 1

i used to love pacman

Answer 2

\[\sum_{n=1}^{infinity} (-1)^n * n / \ln(n)\]

Answer 3

xD Hahaha!

Answer 4

those terms to not even go to zero if i am reading it right

Answer 5

n=2*

Answer 6

It is ((-1)^n * n) in the numerator.

Answer 7

they do alternate, and if they alternate all you need is that they go to zero q

Answer 8

but
\[\lim_{n\to \infty}\frac{n}{\ln(n)}=\infty\]

Answer 9

Oh.

Answer 10

So it diverges, how would we show that b_n approaches infinty?

Answer 11

show ?

Answer 12

I mean it is obvious but do we have to show it? or can we just state it?

Answer 13

it is obvious
\(n\) grows way way (way) faster than \(\ln(n)\)

Answer 14

Alrighty! Thanks :)

Answer 15

for example
\[\frac{1,000,000,000}{\ln(1,000,000,000}=\frac{1,000,000,000}{21}\]

Answer 16

course if your teacher is a real pain, you could use l'hopital but it seems unnecessary to me