According to Wolfram, .
What happens as ?
Hi guys, I am currently doing my homework in limits and derivatives, and there is one question that I'm stuck at. I think the correct answer is 0 but still want to ask for you guys' advice and thoughts
I am quite skeptical about the functions inside the square brackets ... somehow I think they resemble a series, am I right? I wonder if that series has anything to do with this kind of limit. Any suggestions is highly appreciated. Thanks everyone.
As n goes to infinity (think Riemann sums here):
(1/n)[sin(pi/n)+sin(2pi/n+...+sin(npi/n)] -> integral sin(pi x) dx from 0 to 1
so:
sin(pi/n)+sin(2pi/n+...+sin(npi/n) = O(n)
That is the thing diverges.
(In fact sin(pi/n)+sin(2pi/n+...+sin(npi/n) ~= 2n/pi for large n)
CB