question about reduction formula posted below. Anyone with knowledge on calculus are welcomed!

Question

caozeyuan · Answer

Let $$I _{n}= \int\limits_{0}^{1} x ^{n}\left( 1-x \right)^{\frac{ 1 }{ 2}}dx$$

caozeyuan · Answer

Show that, $$n \ge 1, \left( 3+2n \right)I _{n}=2nI _{n-1}$$

caozeyuan · Answer

Hence found the exact value of I subscript 3

caozeyuan · Answer

@amistre64

caozeyuan · Answer

@terenzreignz

terenzreignz · Answer

Where have I 'seen' you before...? name looks familiar

terenzreignz · Answer

Regardless... I know next-to-nothing about reduction formulas... however, let's have a look see at this :D

caozeyuan · Answer

If you are living in Beijing, then you might know me personally

terenzreignz · Answer

Unlikely... besides, my grandparents are (originally) from Guangzhou XD

terenzreignz · Answer

Back to the question...

caozeyuan · Answer

terenzreignz · Answer

^That's like a spoiler... I will resist clicking on that link :D

caozeyuan · Answer

@Loser66 ， Aha! another great mathematician comes online!

caozeyuan · Answer

Are you serious, or just kidding

terenzreignz · Answer

About what?

caozeyuan · Answer

terenzreignz · Answer

And to think I was having a real good think XD

terenzreignz · Answer

Although the solution seems very straightforward.