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Question
Mathematics
The total number of terms in the expansion of ( 1 + x ) 2n - ( 1 - x ) 2n after simplification is
Q. The total number of terms in the expansion of
(
1
+
x
)
2
n
−
(
1
−
x
)
2
n
after simplification is
3860
254
AMU
AMU 2012
Binomial Theorem
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A
n + 1
27%
B
n - 1
21%
C
n
36%
D
4n
16%
Solution:
(
1
+
x
)
2
n
−
(
1
−
x
)
2
n
=
(
2
n
C
0
+
2
n
C
1
x
+
2
n
C
2
x
2
+
+
2
n
C
2
n
x
2
n
)
−
(
2
n
C
0
−
2
n
C
1
x
+
2
n
C
2
x
2
−
2
n
C
3
x
3
+
(
−
1
)
n
2
n
C
2
n
x
2
n
)
=
2
{
2
n
C
1
x
+
2
n
C
3
x
3
+
+
2
n
C
2
n
−
1
(
x
)
2
n
−
1
}
Hence, total number of terms is
n
.