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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
)
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B
(
n
+
1
)
(
n
+
2
)
(
n
+
3
)
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C
n
(
n
+
1
)
(
2
n
+
1
)
6
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D
n
(
4
n
2
−
1
)
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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
)
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Similar questions
Q.
The sum to
n
terms of the series
(
1
×
2
×
3
)
+
(
2
×
3
×
4
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+
(
3
×
4
×
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+
…
is
Q.
If
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is a positive integer, show that
(1)
n
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;
(2)
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(
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n
+
(
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+
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2
!
(
n
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2
)
n
−
⋯
=
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the series in each case being extended to
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terms; and
(3)
1
n
−
n
2
n
+
n
(
n
−
1
)
1
⋅
2
3
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⋯
=
(
−
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) + ...............................................:
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