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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_1 x + C_2 x^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
1
2
+
C
3
4
+
C
5
6
+
⋯
=
2
n
−
1
n
+
1
\frac{C_1}{2} + \frac{C_3}{4} + \frac{C_5}{6} + \dots = \frac{2^n-1}{n+1}
2
C
1
+
4
C
3
+
6
C
5
+
⋯
=
n
+
1
2
n
−
1
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