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Mathematics
Mathematics
Problem
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
⋯
+
C
n
x
n
(1+x)^n = C_0 + C_1x + C_2x^2 + \dots + C_n x^n
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
⋯
+
C
n
x
n
, prove that
C
0
+
3
C
1
+
5
C
2
+
⋯
+
(
2
n
+
1
)
C
n
=
(
n
+
1
)
2
n
C_0 + 3C_1 + 5C_2 + \dots + (2n+1)C_n = (n+1)2^n
C
0
+
3
C
1
+
5
C
2
+
⋯
+
(
2
n
+
1
)
C
n
=
(
n
+
1
)
2
n
.
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