Let In=∫0π/2sinn(x)dxI_n = \int_0^{\pi/2} \sin^n(x) dxIn=∫0π/2sinn(x)dx. Which recurrence relation is correct?
In=n−1nIn−1I_n = \frac{n-1}{n} I_{n-1}In=nn−1In−1
In=n−1nIn−2I_n = \frac{n-1}{n} I_{n-2}In=nn−1In−2
In=nn−1In−2I_n = \frac{n}{n-1} I_{n-2}In=n−1nIn−2
In=nIn−1I_n = n I_{n-1}In=nIn−1