Изменения

<tex>\Phi_n(t)=\frac{1}{n+1}\sum\limits_{k=0}^{n}\frac{1}{2\pi}\frac{ \sin{(k+\frac{1}{2})t}} {\sin{\frac{t}{2}}}=\frac{1}{2\pi(n+1)}\frac{1}{\sin^2{\frac{t}{2}}}\sum\limits_{k=0}^{n}(\sin{((k+\frac{1}{2})t)}\sin{\frac{t}{2}})=</tex> <tex> \frac{1}{2\pi(n+1)}\frac{1}{\sin^{2} \frac{t}{2}}}\sum\limits_{k=0}^{n}\frac{1}{2}(\cos{kt}-\cos{(k+1)t})=\frac{1}{2\pi(n+1)}\frac{1-\cos{(n+1)t}}{2\sin^2{\frac{t}{2}}}=</tex> <tex>\frac{1}{2\pi(n+1)}\frac{\sin^2{\frac{n+1}{2}t}}{\sin^2{\frac{t}{2}}}</tex>