Use the series comparison theorem to prove absolute convergence for all x. Compare with a p-series. I'll leave it to you to figure out which p to useOriginally Posted by augury
Note that I have changed n to k. It's possible that Stewart has a misprint here. In any case that is what is intended.but the series of derivatives diverges when , k is an integer.
First find a formula for . Then evaluate it at (it's the same value at ). Then write down the resulting series. You should then have a p-series that is known to diverge.
Find a formula for . Then use the series divergence test. The series diverges at "most" points, but there are infinitely many values where the series converges; is one of them. Proving the convergence at all these points should turn out to be completely trivialFor what values of x does the series converge?
How about asking the prof? That's what he is getting paid for.I asked the only other student in the class I know and he couldn't do it either. So any help would be greatly appreciated.
Btw, this is not a power series. It's what is called a trigonometric series.