2. Find the term independent of x in the expansion of (x^2 +1/x)^12
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Step-by-step explanation:
MATHS
Find the term independent of x in the expansion of (x
2
+
x
1
)
9
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ANSWER
We have T
r+1
=n
C
r
x
n−r
a
r
where n=9
T
r+1
=9
C
r
(x
2
)
9−r
(
x
1
)
r
=9
C
r
x
18−2r
x
−r
=9
C
r
x
18−2r−r
=9
C
r
x
18−3r
Independent term ⇒18−3r=0
⇒3r=18
⇒r=
3
18
=6
∴ the independent term=T
7
=9
C
6
=
6!3!
9!
=
6!×3×2×1
9×8×7×6!
=
3×2
9×8×7
=3×4×7=84
∴ the term independent of x is T
7
=84
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