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Byju's Answer
Standard V
Mathematics
Roman Numerals
what is the v...
Question
what is the value of1
2
+2
2
+3
2+
+4
2
+5
2
+6
2
+7
2
+8
2
Open in App
Solution
We know that
∑
n
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
so
using
this
property
,
We
can
write
1
2
+
2
2
+
3
2
+
4
2
+
5
2
+
6
2
+
7
2
+
8
2
=
∑
n
=
1
n
=
8
n
2
Here
n
=
8
∑
n
=
1
n
=
8
n
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
=
8
(
8
+
1
)
(
2
×
8
+
1
)
6
=
8
×
9
×
17
6
=
204
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0
Similar questions
Q.
1
2
+
2
2
−
3
2
+
4
2
+
5
2
−
6
2
+
7
2
+
8
2
−
9
2
+
.
.
.
.
to
3
n
terms.
Q.
Using the given pattern, find the missing numbers.
1
2
+
2
2
+
2
2
=
3
2
2
2
+
3
2
+
6
2
=
7
2
3
2
+
4
2
+
12
2
=
13
2
4
2
+
5
2
+
.
.
.
.
.
.
=
21
2
5
2
+
.
.
.
.
.
+
30
2
=
31
2
6
2
+
7
2
+
.
.
.
.
.
.
=
.
.
.
.
.
.
.
.
Q.
Using the given pattern, find the missing numbers:
1
2
+
2
2
+
2
2
=
3
2
2
2
+
3
2
+
6
2
=
7
2
3
2
+
4
2
+
12
2
=
13
2
4
2
+
5
2
+
___
=
21
2
5
2
+
___
+
30
2
=
31
2
6
2
+
7
2
+
___
=
____
Q.
What is the value of (
2
2
+
4
2
+
6
2
+
.
.
.
+
20
2
)-(
1
2
+
3
2
+
5
2
+
.
.
.
+
19
2
)?
Q.
The value of
1
2
−
2
2
+
3
2
−
4
2
+
5
2
−
6
2
+
.
.
.
.
+
99
2
−
100
2
is
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