Изменения

<tex>I_n = \int\limits_0^{\pi/2} \sin^n x dx = </tex> <tex>\int\limits_0^{\pi/2}\sin^{n - 1} x d(-\cos x) = </tex>

<tex>-\sin^{n -1}\cos x|^{\pi/2}_0 + \int\limits_0^{\pi/2} \cos x d \sin^{n-1}x = </tex>

<tex>(n - 1)\int\limits_0^{\pi/2} \sin^{n - 2} x (1-\sin^2x)dx = </tex>

<tex>(n - 1)(I_{n - 2} - I_n)</tex>