2
You visited us
2
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard IX
Mathematics
Ratio and Proportion
The value of ...
Question
The value of
∑
n
r
=
1
(
−
1
)
r
+
1
n
C
r
r
+
1
is equal to
A
−
1
n
+
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
−
1
n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1
n
+
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
n
n
+
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is
D
n
n
+
1
we know that
(
1
−
x
)
n
=
∑
n
r
=
0
n
C
r
(
−
x
)
r
by integrating
∫
1
0
(
1
−
x
)
n
d
x
=
∫
1
0
∑
n
r
=
0
n
C
r
(
−
1
)
r
x
r
d
x
−
[
−
1
n
+
1
]
=
[
∑
n
r
=
0
n
C
r
(
−
1
)
r
x
r
+
1
r
+
1
]
1
0
⇒
1
n
+
1
=
n
C
0
(
−
1
)
0
0
+
1
−
∑
n
r
=
1
n
C
r
(
−
1
)
r
+
1
r
+
1
⇒
∑
n
r
=
1
n
C
r
(
−
1
)
r
+
1
r
+
1
=
1
−
1
n
+
1
=
n
n
+
1
Ans: D
Suggest Corrections
0
Similar questions
Q.
Assertion :
For
n
∈
N
, let
C
r
=
(
n
r
)
,
0
≤
r
≤
n
∑
n
r
=
1
(
r
)
C
2
r
=
n
(
2
n
−
1
n
−
1
)
Reason:
∑
n
r
=
1
C
2
r
=
(
2
n
n
)
Q.
The value of
n
∑
r
=
0
(
−
1
)
r
n
C
r
r
+
2
is equal to .