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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_1 x + C_2 x^2 + C_3 x^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
+
C
n
+
1
x
n
+
1
+
…
C_{n+1} x^{n+1} + \dots
C
n
+
1
x
n
+
1
+
…
, find the values of a.
(
i
)
C
0
−
C
2
+
C
4
−
C
6
+
…
(i) C_0 - C_2 + C_4 - C_6 + \dots
(
i
)
C
0
−
C
2
+
C
4
−
C
6
+
…
b.
(
i
i
)
C
1
−
C
3
+
C
5
−
C
7
+
…
(ii) C_1 - C_3 + C_5 - C_7 + \dots
(
ii
)
C
1
−
C
3
+
C
5
−
C
7
+
…
c.
(
i
i
i
)
C
0
+
C
3
+
C
6
+
…
(iii) C_0 + C_3 + C_6 + \dots
(
iii
)
C
0
+
C
3
+
C
6
+
…
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