Find the term that doesn't have x , of the development (x^2+1/x)^9.

To determine this term, we'll have to write the formula of
the term that occupies the place k+1:

T k+1 =
C(n,k)*a^(n-k)*b^(k) (*)

We'll identify the terms a and b
from the development:

a = x^2 and b =
1/x

We don't know the place that the term occupies, so,
we'll have to determine k.

n =
9

We'll substitute all we know in the formula
(*);

T k+1 =
C(9,k)*x^[2(9-k)]*x^(-k)

We'll add the superscripts of
x:

T k+1 =
C(9,k)*x^[2(9-k)-k]

Since this term doesn't contain x,
we'll impose the constraint that the superscript to be zero, because x^0 =
1.

[2(9-k)-k] = 0

We'll remove
the brackets:

18 - 2k - k =
0

We'll combine like
terms:

-3k = -18

We'll divide
by -3:

k =
6

The term that doesn't
contain x occupies the 7th place, so it is the 7th term of
development.