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Byju's Answer
Standard X
Mathematics
Common Difference
Find the sum ...
Question
Find the sum of
1
2
+
3
2
+
5
2
+
7
2
+
⋯
to
n
terms.
Open in App
Solution
Sum of the square of
n
natural number will be
1
2
+
2
2
+
3
2
+
4
2
+
.
.
.
+
n
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
Thus sum of square of
2
n
natural number wil be
1
2
+
2
2
+
3
2
+
4
2
+
.
.
.
+
(
2
n
)
2
=
2
n
(
2
n
+
1
)
(
4
n
+
1
)
6
1
2
+
3
2
+
.
.
+
(
2
n
−
1
)
2
=
(
1
2
+
2
2
+
3
2
+
4
2
+
.
.
.
+
(
2
n
−
1
)
2
+
(
2
n
)
2
)
−
(
2
2
+
4
2
+
.
.
.
+
(
2
n
)
2
)
1
2
+
3
2
+
.
.
+
(
2
n
−
1
)
2
=
2
n
(
2
n
+
1
)
(
4
n
+
1
)
6
−
2
2
(
1
2
+
2
2
+
3
2
+
4
2
+
.
.
.
+
n
2
)
1
2
+
3
2
+
.
.
+
(
2
n
−
1
)
2
=
2
n
(
2
n
+
1
)
(
4
n
+
1
)
6
−
2
2
n
(
n
+
1
)
(
2
n
+
1
)
6
1
2
+
3
2
+
.
.
+
(
2
n
−
1
)
2
=
2
n
(
2
n
+
1
)
[
(
4
n
+
1
)
−
2
(
n
+
1
)
]
6
1
2
+
3
2
+
.
.
+
(
2
n
−
1
)
2
=
n
(
2
n
+
1
)
(
2
n
−
1
)
3
1
2
+
3
2
+
.
.
+
(
2
n
−
1
)
2
=
n
(
4
n
2
−
1
)
3
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