Using-Riemann-s-sum-calculate-lim-b-n-1-n-k-0-n-1-cos2-kn-n-

Question Number 172311 by mathocean1 last updated on 25/Jun/22

U s i n g {R i e m a n n}^{'} s s u m, c a l c u l a t e :

l i m b_{n} = \frac{1}{n} \sum_{k = 0}^{n - 1} c o s 2 (\frac{k n}{n})

Commented by JDamian last updated on 25/Jun/22

!!! \frac{k n}{n} = k

Commented by thfchristopher last updated on 25/Jun/22

May I ask whether it can prove this :

\cos^{n} x = \frac{1}{2^{n + 1}} \underset{k = 0}{\sum^{(n - 1) / 2}} C_{k}^{n} \cos (n - 2 k) x

where n is any odd number .

Commented by aleks041103 last updated on 25/Jun/22

S e e Q . 170800 .

S e e Q . 170800 .

Commented by thfchristopher last updated on 25/Jun/22

Thank you, sir .

Thank you, sir .