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

$$Using{Riemann}^{\prime }ssum,calculate:$$$$lim{b}_n=\frac{1}{n}\sum _{k=0}^{n-1}cos2\left(\frac{kn}{n}\right)$$

Commented by JDamian last updated on 25/Jun/22

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

Commented by thfchristopher last updated on 25/Jun/22

$$\mathrm{May}\mathrm{I}\mathrm{ask}\mathrm{whether}\mathrm{it}\mathrm{can}\mathrm{prove}\mathrm{this}:$$$${\cos }^{n}x=\frac{1}{2^{n+1}}\underset{k=0}{\sum ^{(n-1)/2}}{C}_k^n\cos (n-2k)x$$$$\mathrm{where}n\mathrm{is}\mathrm{any}\mathrm{odd}\mathrm{number}.$$

Commented by aleks041103 last updated on 25/Jun/22

$$SeeQ.170800.$$

Commented by thfchristopher last updated on 25/Jun/22

$$\mathrm{Thank}\mathrm{you},\mathrm{sir}.$$

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