Hi everyone. First time trying a forum let alone PhysicsForums.com, everyone seems very nice here.
I am trying to figure out whether a sequence is convergent or not by writing out the first 5 terms. The sequence is: sin[1+(pi/n)]+nsin(pi/n).
I can't seem to show the limit of the above determined sequence, after finding it is in fact convergent.
The Attempt at a Solution
As I let n=1,2,3,4,5 I got 0.127, 0.0997, 0.0905, 0.0860, 0.0832 respectively.
Now this seems to be heading toward a limit but determining the limit is where I am going wrong, I believe. I sort of cheated and substituted n=1000, 10000 and 1000000 and got 0.07233, 0.07228 and 0.07228 again from the graphics calculator.
Now I believe the limit is approx. 0.0722... but how could I possibly go about finding this from the original sequence?