find the ratio of expansion of 5th and 3rd term of expansion of (2+x)⁵
Answers
Answer:
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Step-by-step explanation:
(3x−
x
2
1
)
10
As we know that generalt term of expnsion (a+b)
n
is-
T
r+1
=
n
C
r
a
n−r
b
n
In the given expansion-
(3x−
x
2
1
)
10
n=10
a=3x
b=−
x
2
1
Therefore, general term of the given epansion will be-
T
r+1
=
10
C
r
(3x)
10−r
(
x
2
1
)
r
⇒T
r+1
=
10
C
r
(3
10−r
)(x
10−r
)(
x
2r
1
)
⇒T
r+1
=
10
C
r
(3
10−r
)(x
10−3r
).....(1)
As we know that,
p
th
term form end =(n−p+2)
th
term from starting.
∴5
th
term form end =(10−5+2)
th
=7
th
term from starting.
∴T
7
=T
6+1
⇒r=6
Substituting the value of r in eq
n
(1), we have
T
6+1
=
10
C
6
(3
10−6
)(x
10−(3×6)
)
⇒T
7
=
10
C
6
(3
4
)(x
−8
)
Hence the 5
th
term from the end in the given expansion will be 7
th
term from the starting, i.e.,
10
C
6
(3
4
)(x
−8
).