Let In=the integral from 0 to pi/2 of sinnxdx
show that (I2n+1)/(I2n)=(2n+1)/(2n+2)
integral from 0 to pi/2 of sin2n=(2n-1)pi/4n
The Attempt at a Solution
I can't write down all that I've done because it's just too ridiculous. I've tried lots of forms of just trying to manipulate my equation above, which didn't work. I've tried integration by parts for sin2n+1*sinx but I've ended up with the integral of cos2xsin2nx and I can't find a suitable substitution for that. I've been working on this problem forever and it's killing me. If anyone has any suggestions I would be very appreciative.