10
You visited us
10
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Arithmetic Mean
If sum of n t...
Question
If sum of n terms of a series is given by
n
(
n
+
1
)
(
n
+
2
)
(
n
+
3
)
4
then the
n
th term of the series is
A
n
(
n
+
1
)
(
n
+
2
)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
(
n
+
1
)
(
n
+
2
)
(
n
+
3
)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
n
(
n
+
1
)
(
2
n
+
1
)
6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
n
(
4
n
2
−
1
)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
A
n
(
n
+
1
)
(
n
+
2
)
Given
S
n
=
n
(
n
+
1
)
(
n
+
2
)
(
n
+
3
)
4
∴
t
n
=
S
n
−
S
n
−
1
=
n
(
n
+
1
)
(
n
+
2
)
(
n
+
3
)
4
−
(
n
−
1
)
n
(
n
+
1
)
(
n
+
2
)
4
=
n
(
n
+
1
)
(
n
+
2
)
4
[
n
+
3
−
n
+
1
]
=
n
(
n
+
1
)
(
n
+
2
)
Suggest Corrections
0
Similar questions
Q.
The sum to
n
terms of the series
(
1
×
2
×
3
)
+
(
2
×
3
×
4
)
+
(
3
×
4
×
5
)
+
…
is
Q.
If
n
is a positive integer, show that
(1)
n
n
+
1
−
n
(
n
−
1
)
n
+
1
+
n
(
n
−
1
)
2
!
(
n
−
2
)
n
+
1
−
⋯
=
1
2
n
(
n
+
1
)
!
;
(2)
n
n
−
(
n
+
1
)
(
n
−
1
)
n
+
(
n
+
1
)
n
2
!
(
n
−
2
)
n
−
⋯
=
1
;
the series in each case being extended to
n
terms; and
(3)
1
n
−
n
2
n
+
n
(
n
−
1
)
1
⋅
2
3
n
−
⋯
=
(
−
1
)
n
n
!
;
(4)
(
n
+
p
)
n
−
n
(
n
+
p
−
1
)
n
+
n
(
n
−
1
)
2
!
(
n
+
p
−
2
)
n
−
⋯
=
n
!
;
the series in the last two cases being extended to
n
+
1
terms.
Q.
If n is a multiple of
6
, show that each of the series
n
−
n
(
n
−
1
)
(
n
−
2
)
⌊
3
⋅
3
+
n
(
n
−
1
)
(
n
−
2
)
(
n
−
3
)
(
n
−
4
)
⌊
5
⋅
3
2
−
.
.
.
.
.
,
n
−
n
(
n
−
1
)
(
n
−
2
)
⌊
3
⋅
1
3
+
n
(
n
−
1
)
(
n
−
2
)
(
n
−
3
)
(
n
−
4
)
⌊
5
⋅
1
3
2
−
.
.
.
.
.
,
is equal to zero.
Q.
The sum of the series
1
×
n
+
2
(
n
−
1
)
+
3
(
n
−
2
)
+
…
…
+
(
n
−
1
)
×
2
+
n
×
1
is
Q.
Find the sum to n terms of the series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ...............................................:
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
Arithmetic Progression
MATHEMATICS
Watch in App
Explore more
Arithmetic Mean
Standard XII 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