Question

The coefficient of x^ky^n-k in the expansion of (x+y)^n equals (n-k/k).
A.True
B.false.

Answer 1

The statement about the coefficient of x^k*y^(n-k) in the expansion of (x+y)^n being (n-k/k) is false. The correct coefficient is determined using the binomial coefficient n choose k, not (n-k/k).

Step-by-step explanation:

The statement about the coefficient of xkyn-k in the expansion of (x+y)n is false. According to the binomial theorem, the general term in the expansion of (a+b)n is given by:

Tr+1 = C(n, r) · an-rbr

For the term xkyn-k, we have r = k and therefore the coefficient would be C(n, k) = n! / [k! · (n-k)!], where C(n, k) is the binomial coefficient. Hence, the correct coefficient would be (nchoosek), not (n-k/k). The binomial coefficient is usually represented as n choose k (nCk).