Help Pls with this Q (1 Viewer)

[Modern4DaBois]

I get the first two parts. Those are ez. But how would you go about proving the third one? @jimmysmith560 help lol

 

[idkkdi]

View attachment 35090
I get the first two parts. Those are ez. But how would you go about proving the third one? @jimmysmith560 help lol

LHS = (-1)^n
= (1+w)^3n
= RHS

Cancel out the 3nCm, mEZ, 3|m terms.

1/2((Rhs - those terms)x2)
= 1/2 ((3nC1 w+3nC3n-1 w^2) (was w^3n-1) + (3nC2 w+3nC3n-2 w^2) +...... ), for terms higher than w^3, divide by w^3k, kEZ to get either w or w^2
Using part i), and the nCm = nCn-m identity
= 1/2 (-3nC1 - 3nC2 - 3nC4 - 3nC5 .....)
= LHS - those terms

 

[jimmysmith560]

Would the following working help?