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Byju's Answer
Standard XII
Mathematics
Middle Terms
The numerical...
Question
The numerical value of middle terms in
(
1
−
1
x
)
n
(
1
−
x
)
n
is
A
2
n
C
n
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B
n
C
n
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C
(
2
n
C
n
)
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D
(
n
C
n
)
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Solution
The correct option is
A
2
n
C
n
(
1
−
1
x
)
n
(
1
−
x
)
n
=
(
x
−
1
)
n
x
n
(
1
−
x
)
n
=
(
−
1
)
n
x
n
(
1
−
x
)
2
n
middle term =
T
n
+
1
=
(
−
1
)
n
x
n
.
2
n
C
n
(
1
)
2
n
−
n
(
−
x
)
n
=
(
−
1
)
n
x
n
.
2
n
C
n
.1
.
(
−
1
)
n
.
x
n
middle term =
(
−
1
)
2
n
.
2
n
C
n
Suggest Corrections
0
Similar questions
Q.
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
.
.
.
+
C
n
x
n
, then
2
C
0
+
2
2
.
C
1
2
+
2
3
.
C
2
3
+
.
.
.
+
2
n
+
1
.
C
n
n
+
1
=
Q.
c
0
,
c
1
,
c
2
denotes coefficents expansion of
(
1
+
x
)
n
, then
c
1
+
c
1
c
2
+
c
2
c
3
+
.
.
.
.
.
.
.
c
n
−
1
c
n
=
(
2
n
)
!
(
n
+
1
)
!
(
n
−
1
)
!
Q.
If
c
0
,
c
1
,
c
2
,
.
.
.
.
.
.
.
c
n
denote the coefficients in the expansion of
(
1
+
x
)
n
, prove that
c
0
c
r
+
c
1
c
r
+
1
+
c
2
c
r
+
2
+
.
.
.
.
+
c
n
−
r
c
n
=
|
2
n
–
–
–
|
n
−
r
–
––––
–
|
n
+
r
–
––––
–
.
Q.
If
c
0
,
c
1
,
c
2
,
.
.
.
.
.
.
.
c
n
denote the coefficients in the expansion of
(
1
+
x
)
n
, prove that
c
0
+
c
1
2
+
c
2
3
+
.
.
.
.
.
.
+
c
n
n
+
1
=
2
n
+
1
−
1
n
+
1
.
Q.
If
c
0
,
c
1
,
c
2
,
.
.
.
.
c
n
denote the coefficients in the expansion of
(
1
+
x
)
n
, prove that
c
0
+
c
1
2
+
c
2
3
+
.
.
.
.
.
+
c
n
n
+
1
=
2
n
+
1
−
1
n
+
1
.
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