Question

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

Answer 1

the given statement is false

Answer 2

The given statement is false.

Explanation:

Given : The coefficient of
`x^k y^(n-k)` in the expansion of
`(x+y)^n` equals
`(n-k)/(k)`.

To find : True or False

Solution : The given statement is not true .

Because, when we do expansion of
`(x+y)^n` by binomial theorem we get,

`(x+y)^n= ^(n)C_k x^k y^(n-k)`

Therefore, coefficient of
`x^k y^(n-k)` is
`^(n)C_k=(n!)/((n-k)!k!)`

The given statement is false.