Does anyone understand raabe's test of convergence?

Question

epoweritheta · Answer

I am reading that now , wait a minute ...

anonymous · Answer

Okay thank you!

anonymous · Answer

Any luck? :)

epoweritheta · Answer

ya... 1 minute ... i am going to finish it

anonymous · Answer

alright thank you

epoweritheta · Answer

see this link this has easy proof of raabe's test : https://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CC8QFjAB&url=http%3A%2F%2Fthep.housing.rug.nl%2Fsites%2Fdefault%2Ffiles%2Fusers%2Fuser12%2FRaabe_test.pdf&ei=IROVU4aOOdSKuATi4IDYAQ&usg=AFQjCNHkfE21UBusZLGW2YXQSdWkOczMSw&sig2=s7_dolmlSh9xkB1tRgWTnw&bvm=bv.68445247,d.c2E

anonymous · Answer

Can you give me an example please? general solution, not detailed. im sorry if it'll bother you

epoweritheta · Answer

no problem...
lets solve this problem

anonymous · Answer

okay :)

epoweritheta · Answer

now what is $$\left| \frac{ Un }{ Un+1 } \right| $$ 
tell me

anonymous · Answer

$$\frac{ 2n }{ 2n+3 }??$$

epoweritheta · Answer

again do it , i get a different answer check again

anonymous · Answer

you know i think it's fine, i won't understand it but its fine, thank you soo much though!

epoweritheta · Answer

check again u will get $$\left| \frac{ Un }{ Un+1} \right| = \frac{ 2n+4 }{ 2n+1 }$$

anonymous · Answer

ya i understand my mistake now :P

epoweritheta · Answer

ie = 1+3/2n+1 
then we have 
$$n*(\left| \frac{ Un }{ Un+1 } \right| -1) = n*\frac{ 3 }{ 2n+1 }=\frac{ 3 }{ 2+1/n }$$

note when is large n(|Un/Un+1| -1) >1 therefore is convergent

epoweritheta · Answer

if the same thing is less than 1 , then it is divergent , if =1 ,then we cant conclude anything from this test

anonymous · Answer

wow, It's actually really easy! THANK YOU!! :D

epoweritheta · Answer

:D