Show that the series  does not converge uniformly on the interval 

To show that the series \(\sum_{n=1}^{\infty }\frac{\sin n\theta}{n}\) does not converge uniformly on the interval \(]0, 2\pi[\), we can use the Dirichlet's Test.

Dirichlet's Test states that if:

1. The sequence of partial sums of the series \(\sum_{n=1}^{\infty} a_n\) is bounded, i.e., \(\left|\sum_{k=1}^{n}a_k\right|\) is bounded for _________ ________ _________ _______ _______ ______.
_______ ________ __________ __________ _____ ______ _____ ________ ______ ______ _______ ______.
_________ _____ _________ _________ ___ _________ ________ __________.
________ _________ _________ ________ _______ ________ ________ _____ ___ _________.
____ ______ ____ _________ _____ ____ _______ __________ _________ _____ ____.
_______ ________ __________ ________ ______ _____ _______ _____ ____ __________ ________.
________ ________ ________ ________ ____ ___ _____ _____ ______ ___.
__________ __________ __________ _______ ________ _______ _______ _____.
_______ _______ _______ _________ ____ ___ ___ ________ _________ ____ _____ _________.
___ __________ __________ _________ ___ _____ _______.
_____ ___ _______ ____ __________ ______ ______ _______.
_____ ______ _______ _____ __________ _________ __________.
__________ ____ _____ _________ ______ ______ ______ _________ _____.
______ ________ _______ ____ ____ _______ ___ ____.
______ ___ ___ _________ ________ _____ ______ ________ ________ ________ __________.
_______ _________ ______ _____ _____ _________ _________.
_______ ________ __________ _________ _______ _______ __________ __________ _________ __________.
_____ ___ _______ _________ __________ _____ __________ ________ __________ ________ ___.
_______ ______ __________ ___ ____ _____ _________ ____ __________.
__________ ______ ________ ______ ___ ___ _______ _______ __________ ____ ____.
Get Full Answer on WhatsApp