3
You visited us
3
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XIII
Mathematics
Sum of Coefficients of All Terms
If 1+xn=C0+C1...
Question
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
…
+
C
n
x
n
,
then the value of
∑
∑
0
≤
r
<
s
≤
n
(
C
r
+
C
s
)
2
is
A
(
n
−
1
)
⋅
2
n
C
n
−
2
2
n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(
n
+
1
)
⋅
2
n
C
n
+
2
2
n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(
n
+
1
)
⋅
2
n
C
n
−
2
2
n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(
n
−
1
)
⋅
2
n
C
n
+
2
2
n
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is
D
(
n
−
1
)
⋅
2
n
C
n
+
2
2
n
We have,
∑
∑
0
≤
r
<
s
≤
n
(
C
r
+
C
s
)
2
=
(
C
0
+
C
1
)
2
+
(
C
0
+
C
2
)
2
+
…
+
(
C
0
+
C
n
)
2
+
(
C
1
+
C
2
)
2
+
(
C
1
+
C
3
)
2
+
…
.
+
(
C
1
+
C
n
)
2
+
⋮
+
⋮
+
⋯
+
⋮
+
(
C
n
−
2
+
C
n
−
1
)
2
+
(
C
n
−
2
+
C
n
)
2
+
(
C
n
−
1
+
C
n
)
2
=
n
(
C
2
0
+
C
2
1
+
…
+
C
2
n
)
+
2
∑
∑
0
≤
r
<
s
≤
n
C
r
C
s
=
n
⋅
2
n
C
n
+
[
2
2
n
−
2
n
C
n
]
=
(
n
−
1
)
⋅
2
n
C
n
+
2
2
n
Suggest Corrections
0
Similar questions
Q.
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
.
.
.
+
C
n
x
n
, then the value of
C
0
−
C
1
+
C
2
−
C
3
+
.
.
.
+
(
−
1
)
n
C
n
is -`
Q.
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
⋅
⋅
⋅
⋅
⋅
+
C
n
x
n
, then
Q.
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
.
.
.
+
C
n
x
n
, then
C
0
C
2
+
C
1
C
3
+
C
2
C
4
+
.
.
.
+
C
n
−
2
C
n
=
Q.
If
(
1
+
x
)
n
=
C
0
+
C
1
x
+
C
2
x
2
+
.
.
.
.
.
.
.
.
.
.
+
C
n
x
R
, then the sum
C
0
+
(
C
0
+
C
1
)
+
(
C
0
+
C
1
+
C
2
)
+
.
.
.
.
.
+
(
C
0
+
C
1
+
C
2
+
.
.
.
.
.
+
C
n
−
1
is
Q.
If
(
1
+
x
)
n
=
n
∑
r
=
0
C
r
x
r
, the value of
C
0
+
(
C
0
+
C
1
)
+
(
C
0
+
C
1
+
C
2
)
+
⋯
(
C
0
+
C
1
+
C
2
+
⋯
+
C
n
−
1
)
equals
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Sum of Coefficients of All Terms
MATHEMATICS
Watch in App
Explore more
Sum of Coefficients of All Terms
Standard XIII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app