ln(2n/n+1)
State whether the sequence converges and if it does find the limit.

I'm really having trouble understanding this can someone please explain?

Question

ln(2n/n+1)
State whether the sequence converges and if it does find the limit.

I'm really having trouble understanding this can someone please explain?

anonymous · Answer

do uyou any converges test ?

anonymous · Answer

Im basically having to learn this on my own and I am struggling through this, I am still learning the rule and trends and have not done any converges tests. If someone could give me a step by step walkthrough of how to do the problem it would be greatly appreciated, this is me practicing on my own for the upcoming section theres no grade involved

rational · Answer

use limit test :
$$\lim \limits_{n\to \infty} a_n \ne 0 \implies \text{the series diverges}$$

anonymous · Answer

ratio test wont be easier ?

rational · Answer

evaluate :  $\lim \limits_{n\to \infty}  \ln  \left(\dfrac{2n}{n+1}\right)$

rational · Answer

if that limit is not 0, then that means the terms in the sequence are adding up to the series... so the sum has to diverge ^

rational · Answer

yeah but limit test looks easy for this...

anonymous · Answer

Ok thank you I think I was looking for ways to make it convergent without doing the limit test first and thats what messed me up as I wasn't expecting it to diverge

Thank you!

rational · Answer

yw :) u may verify these wid wolfram... (u wil miss the fun of solving on ur own :P) http://www.wolframalpha.com/input/?i=%5Csum+%5Climits_%7Bn%3D1%7D%5E%7B%5Cinfty%7D+%5Cln%282n%2F%28n%2B1%29%29