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Question
Mathematics
The coefficient of x10 in the expansion of 1+(1+x)+ ldots+(1+x)20 is
Q. The coefficient of
x
10
in the expansion of
1
+
(
1
+
x
)
+
…
+
(
1
+
x
)
20
is
2930
186
WBJEE
WBJEE 2012
Binomial Theorem
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A
19
C
9
11%
B
20
C
10
45%
C
21
C
11
39%
D
22
C
12
4%
Solution:
The given series is in GP. Hence, its sum
S
=
(
1
+
x
)
−
1
1
{
(
1
+
x
)
20
+
1
−
1
}
=
x
(
1
+
x
)
21
−
1
Therefore, the required coefficient of
x
10
in the expansion of
x
(
1
+
x
)
21
−
1
=
Coefficient of
x
11
in the expansion of
(
1
+
x
)
21
−
1
=
21
C
11