Question

alternating series

Answer 1

So i am getting that this converges. but my book says diverges how is this?

Answer 2

on account of the limit of the terms is not zero!

Answer 3

take into account, the alternating series test

Answer 4

you need
\[\lim_{n\to \infty}|a_n|=0\] but in this case it is not

Answer 5

yes i did so! i took the limit of (k+1)/(3k+1) & got 1!

Answer 6

\[\lim_{k\to \infty}\frac{k+1}{3k+1}=\frac{1}{3}\neq 0\]

Answer 7

^ correct! i got to that and got stumped :/

Answer 8

1 is wrong, but even if it was right it still wouldn't converge
the limit must be zero

Answer 9

^there you go
So hence it diverges

Answer 10

oh I'm sorry i meant to put 1/3! sorry

Answer 11

ohh! @OrthodoxMan no wonder it fails that test!

Answer 12

Don't worry, people make mistakes. Use this link if you need more help, here.
http://tutorial.math.lamar.edu/Classes/CalcII/AlternatingSeries.aspx

Answer 13

Thank you both @OrthodoxMan & @satellite73 :)

Answer 14

yw