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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
n
C
1
+
n
C
2
+
⋯
+
n
C
n
=
n
(
n
+
1
)
⋅
2
n
−
2
{}^n C_1 + {}^n C_2 + \dots + {}^n C_n = n(n+1)\cdot 2^{n-2}
n
C
1
+
n
C
2
+
⋯
+
n
C
n
=
n
(
n
+
1
)
⋅
2
n
−
2
.
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