2012 Independent Trials last question (1 Viewer)

[FrankUses]

Question:

I don't get how you do part ii, why do you equate coefficients of x^2 and where does 2C2 + 3C2 + ... come from

 

[Alkanes]

Lol. Remove it before it gets cleaned out by the mods.

 

[FrankUses]

Huh what am I doing wrong?

 

[braintic]

Your strategy: look at the simplest half of the result to prove, ie. nC3, and try to compare it to the simplest half of the result you just proved (the RHS).
nC3 is the coefficient of x^2 in this expression.
So we need to find the coefficient of x^2 in the LHS of the same expression.
There are no x^2 terms in (1+x)^0 or (1+x)^1, but every term thereafter has an x^2 term, and it is always the 3rd term from the start, ie. the kC2 term.
Add these terms from k=2 to k=n-1 and you get the required result.

 

[FrankUses]

Ahh I see Thanks a million. Need to do more practice on binomial theorems