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Mathematics
Mathematics
Problem
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
⋯
+
C
n
x
n
(1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \dots + C_n x^n
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
⋯
+
C
n
x
n
,
n
n
n
being even the value of
C
0
+
(
C
0
+
C
1
)
+
(
C
0
+
C
1
+
C
2
)
+
⋯
+
(
C
0
+
C
1
+
C
2
+
⋯
+
C
n
−
1
)
C_0 + (C_0 + C_1) + (C_0 + C_1 + C_2) + \dots + (C_0 + C_1 + C_2 + \dots + C_{n-1})
C
0
+
(
C
0
+
C
1
)
+
(
C
0
+
C
1
+
C
2
)
+
⋯
+
(
C
0
+
C
1
+
C
2
+
⋯
+
C
n
−
1
)
is equal to a.
n
⋅
2
n
n \cdot 2^n
n
⋅
2
n
b.
n
⋅
2
n
−
1
n \cdot 2^{n-1}
n
⋅
2
n
−
1
c.
n
⋅
2
n
−
2
n \cdot 2^{n-2}
n
⋅
2
n
−
2
d.
n
⋅
2
n
−
3
n \cdot 2^{n-3}
n
⋅
2
n
−
3
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