The coefficient of x^ky^n-k in the expression of (x+y) ^n equals (n-k/k) true or false

False

Step-by-step explanation:

The given statement is:

The coefficient of x^ky^n-k in the expression of (x+y) ^n equals (n-k/k)

This is a false statement

Reason:

When we do expansion of (x+y) ^n by binomial theorem we get the following solution:

(x+y) ^n = nCk x^k y^n-k

This shows that the coefficient of x^ky^n-k is nCk which is equivalent to n! / (n-k) ! k!

Therefore it is a false statement ...