how do i use binomial to show that 3^k C(n,k) = 3^k 1^n-k C(n,k)
Did you type that correctly? Right now you have stuff = stuff * 1, which is clearly correct...
i wanted to explain a bit more
It should be
sum 3^k C(n,k) = 2^2n
the hint is 3^k C(n,k) = 3^k 1^n-k C(n,k)
The reason C(n, k) are called "binomial coefficients" is that C(n, k) is the coefficient of xk in (x+ y)n What are the coefficients of xk in (3x+ y)n? What do you get if x= y= 1?
Separate names with a comma.