Question

What is the coefficient of the last term in the binomial expansion of (x + 1)9?

0
1
9
10

Answer 1

1

Explanation:

Given :
`(x+1)^(9)`

To Find : What is the coefficient of the last term in the binomial expansion of (x + 1)9?

Solution :

Formula of expansion :
`(x+a)^(n) =\sum_(k=0)^(n) _(n) C_k x^(k) a^(n-k)`

`(x+1)^(9) =\sum_(k=0)^(9) _(9) C_k x^(k) a^(9-k)`

So , in the last term k =9

`_(9) C_9 x^(9) a^(9-9)`

`(9!)/(9!*0!)x^(9)`

`1*x^(9)`

Thus the coefficient of last term is 1.

Hence option 2 is correct

Answer 2

The first and last terms have coefficients of 1. The coefficient of the n-th term is C(9, n-1) = 9!/((n-1)!(10-n)!) for n=1 to 10.

The appropriate choice is ...

... 1