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Byju's Answer
Standard XI
Mathematics
Complex Numbers
∑nj=1∑ni=1i i...
Question
∑
n
j
=
1
∑
n
i
=
1
i
is equal to
A
n
(
n
+
1
)
2
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B
n
(
n
+
1
)
2
2
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C
n
2
(
n
+
1
)
2
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D
none of these
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Solution
The correct option is
C
n
2
(
n
+
1
)
2
Given,
∑
n
j
=
1
∑
n
i
=
1
i
here, we use the direct formula
=
∑
n
j
=
1
1
2
n
(
n
+
1
)
=
1
2
n
2
(
n
+
1
)
=
n
2
(
n
+
1
)
2
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0
Similar questions
Q.
Find the value of expression
∑
n
i
=
1
∑
i
j
=
1
∑
j
k
=
1
6.
Q.
The sum of the series
1
×
n
+
2
(
n
−
1
)
+
3
(
n
−
2
)
+
…
…
+
(
n
−
1
)
×
2
+
n
×
1
is
Q.
If
1
×
2
2
+
2
×
3
2
+
3
×
4
2
+
⋯
+
n
(
n
+
1
)
2
1
2
×
2
+
2
2
×
3
+
3
2
×
4
+
⋯
+
n
2
(
n
+
1
)
=
8
7
, then
n
=
Q.
The sum of first
n
terms of the series
1
2
1
+
1
2
+
2
2
1
+
2
+
1
2
+
2
2
+
3
2
1
+
2
+
3
+
⋯
is equal to
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.
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