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Mathematics
Problem
If
(
1
+
x
)
n
=
∑
r
=
0
n
n
C
r
x
r
(1+x)^n = \sum_{r=0}^{n} {}^n C_r x^r
(
1
+
x
)
n
=
∑
r
=
0
n
n
C
r
x
r
,
(
1
+
C
1
C
0
)
(
1
+
C
2
C
1
)
…
(
1
+
C
n
C
n
−
1
)
\left(1 + \frac{C_1}{C_0}\right) \left(1 + \frac{C_2}{C_1}\right) \dots \left(1 + \frac{C_n}{C_{n-1}}\right)
(
1
+
C
0
C
1
)
(
1
+
C
1
C
2
)
…
(
1
+
C
n
−
1
C
n
)
is equal to a.
n
n
−
1
(
n
−
1
)
!
\frac{n^{n-1}}{(n-1)!}
(
n
−
1
)!
n
n
−
1
b.
(
n
+
1
)
n
−
1
(
n
−
1
)
!
\frac{(n+1)^{n-1}}{(n-1)!}
(
n
−
1
)!
(
n
+
1
)
n
−
1
c.
(
n
+
1
)
n
n
!
\frac{(n+1)^n}{n!}
n
!
(
n
+
1
)
n
d.
(
n
+
1
)
n
+
1
n
!
\frac{(n+1)^{n+1}}{n!}
n
!
(
n
+
1
)
n
+
1
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