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Mathematics
Mathematics
Problem
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
(1+x)^n = C_0 + C_1 x + C_2 x^2
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
C
3
x
3
+
.
.
.
+
C
n
x
n
+ C_3 x^3 + ... + C_n x^n
+
C
3
x
3
+
...
+
C
n
x
n
, prove that
C
1
−
2
C
2
+
3
C
3
−
.
.
.
+
(
−
1
)
n
−
1
n
C
n
=
0.
C_1 - 2C_2 + 3C_3 - ... + (-1)^{n-1} n C_n = 0.
C
1
−
2
C
2
+
3
C
3
−
...
+
(
−
1
)
n
−
1
n
C
n
=
0.
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