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Byju's Answer
Standard XI
Mathematics
Sigma n
If i - 1n∑ i ...
Question
If
n
∑
i
−
1
i
=
n
(
n
+
1
)
2
,
t
h
e
n
n
∑
i
−
1
(
3
i
−
2
)
=
A
n
(
3
n
−
1
)
2
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B
n
(
3
n
+
1
)
2
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C
n(3n + 2)
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D
n
(
3
n
+
1
)
4
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Solution
The correct option is
A
n
(
3
n
−
1
)
2
n
∑
i
−
1
=
3
n
∑
i
−
1
i
−
2
n
∑
i
−
1
=
3
n
(
n
+
1
)
2
−
2
n
=
n
(
3
n
−
1
)
2
.
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1
Similar questions
Q.
If
n
∑
i
−
1
i
=
n
(
n
+
1
)
2
,
t
h
e
n
n
∑
i
−
1
(
3
i
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)
=
Q.
If
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, then
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Q.
If
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(
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+
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i
)
(
1
+
3
i
)
.
.
.
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(
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+
n
i
)
=
α
+
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then
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(
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Q.
If
(
1
−
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)
(
1
+
2
i
)
(
1
+
3
i
)
.
.
.
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(
1
+
n
i
)
=
α
+
i
β
then
2
⋅
5
⋅
10
.
.
.
.
(
1
+
n
2
)
=
Q.
If
z
=
(
1
+
i
)
(
1
+
2
i
)
(
1
+
3
i
)
…
…
…
(
1
+
n
i
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(
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(
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i
)
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, where
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∈
N
, then principal argument of
z
can be -
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