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Question
Mathematics
displaystyle∑k=0n (nCk/k+1) =
Q.
k
=
0
∑
n
k
+
1
n
C
k
=
3994
198
COMEDK
COMEDK 2008
Binomial Theorem
Report Error
A
n
+
1
2
n
−
1
24%
B
n
−
1
2
n
−
1
−
1
29%
C
n
+
1
2
n
+
1
−
1
35%
D
n
2
n
−
1
12%
Solution:
k
=
0
∑
n
k
+
1
n
C
k
=
k
=
0
∑
n
(
k
+
1
)
k
!
(
n
−
k
)
!
n
!
=
k
=
0
∑
n
(
k
+
1
)
!
(
n
−
k
)
!
(
n
+
1
)
n
!
(
n
+
1
)
=
n
+
1
1
k
=
0
∑
n
(
k
+
1
)
!
(
n
+
1
−
k
−
1
)
!
(
n
+
1
)
!
=
n
+
1
1
k
=
0
∑
n
n
+
1
C
k
+
1
=
n
+
1
1
[
2
n
+
1
−
1
]