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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_1x + C_2x^2 + C_3x^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
, prove that
C
0
−
2
C
1
+
3
C
2
−
4
C
3
+
⋯
+
(
−
1
)
n
(
n
+
1
)
C
n
=
0
C_0 - 2C_1 + 3C_2 - 4C_3 + \dots + (-1)^n (n+1)C_n = 0
C
0
−
2
C
1
+
3
C
2
−
4
C
3
+
⋯
+
(
−
1
)
n
(
n
+
1
)
C
n
=
0
.
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