Question

The coefficient of xkyn-k in the expansion of (x+y)n equals (n/k) true or false

Answer 1

Answer:

The correct option is 1. The given statement is true.

Step-by-step explanation:

The binomial expansion is defined as

$(x+y)^n=^nC_0x^{n-0}y^{1}+^nC_{1}x^{n-1}y^{2}+....+^nC_{n-1}x^{1}y^{n-1}+^nC_nx^{0}y^{n}$

The rth term in a binomial expansion is defined as

$\text{rth term}=^nC_rx^{n-r}y^{r}$

Let the coefficient of $x^ky^{n-k}$ be A. The power of x is k and the power of y is n-k. It means

$k=n-r$

$n-k=r$

The coefficient of $x^ky^{n-k}$ is

$^nC_{n-k}=\binom{n}{n-k}$

Using the property of combination,

$^nC_{n-r}=^nC_r$

$^nC_{n-k}=^nC_{k}=\binom{n}{k}$

The coefficient of $x^ky^{n-k}$ is $\binom{n}{k}$. Therefore the given statement is true.

Answer 2

The answer to your question is
TRUE -Apex