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Byju's Answer
Standard X
Mathematics
Sum of Squares of First N Natural Numbers
The sum of th...
Question
The sum of the squares of the first n natural
numbers is
A
n
(
n
+
1
)
2
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B
n
(
n
+
1
)
(
2
n
+
1
)
6
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C
n
(
n
+
1
)
(
n
+
2
)
12
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D
n
(
n
+
1
)
(
2
n
+
1
)
12
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Solution
The correct option is
B
n
(
n
+
1
)
(
2
n
+
1
)
6
The formula to find sum of first
n
terms of a sequence of squares of natural numbers
=
n
(
n
+
1
)
(
2
n
+
1
)
6
Suggest Corrections
0
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Q.
Assertion :The variance of first
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2
−
1
6
Reason: The sum and the sum of squares of first
n
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n
(
n
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1
)
2
and
n
(
n
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1
)
(
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Q.
Find the sum to n terms of the series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4) + ...............................................:
Q.
Statement-1 : The variance of first n even natural numbers is
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Statement-2 : The sum of first n natural numbers is
n
(
n
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1
)
2
and The sum of squares first n natural numbers is
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n
+
1
)
(
2
n
+
1
)
6
Q.
Assertion :The variance of the series
a
,
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,
a
+
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d
,
a
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d
,
.
.
.
.
a
+
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n
d
is
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n
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3
d
2
. Reason: The sum and the sum of squares of first
n
natural numbers
n
(
n
+
1
)
2
and
n
(
n
+
1
)
(
2
n
+
1
)
6
respectively
Q.
Assertion :The variance of first
n
even natural numbers is
n
2
−
1
4
. Reason: The sum of first
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