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Byju's Answer
Standard VIII
Mathematics
Adding Triangular Numbers
Observe the f...
Question
Observe the following patterns
1
=
1
2
(
1
×
(
1
+
1
)
)
1
+
2
=
1
2
(
2
×
(
2
+
1
)
)
1
+
2
+
3
=
1
2
(
3
×
(
3
+
1
)
)
1
+
2
+
3
+
4
=
1
2
(
4
×
(
4
+
1
)
)
and find the value of each of the following
31
+
32
+
.
.
.
+
50
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Solution
By observing fpllowing patten
we see that
1
+
2
+
−
−
−
+
n
=
1
2
[
n
×
(
n
=
1
)
]
31
+
32
+
−
−
−
+
50
=
1
+
2
+
3
+
−
−
−
50
−
(
1
+
2
+
−
−
−
+
30
)
=
[
50
×
51
]
−
1
2
[
30
×
31
]
=
1275
−
465
31
+
32
+
−
−
−
+
50
=
810
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0
Similar questions
Q.
Observe the following patterns
1
=
1
2
(
1
×
(
1
+
1
)
)
1
+
2
=
1
2
(
2
×
(
2
+
1
)
)
1
+
2
+
3
=
1
2
(
3
×
(
3
+
1
)
)
1
+
2
+
3
+
4
=
1
2
(
4
×
(
4
+
1
)
)
and find the value of each of the following
1
+
2
+
3
+
4
+
5
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.
.
.
.
+
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Q.
Observe the following pattern
1
=
1
2
1
×
1
+
1
1
+
2
=
1
2
2
×
2
+
1
1
+
2
+
3
=
1
2
3
×
3
+
1
1
+
2
+
3
+
4
=
1
2
4
×
4
+
1
and find the values of each of the following:
(i) 1 + 2 + 3 + 4 + 5 + ... + 50
(ii) 31 + 32 + ... + 50
Q.
Observe the following pattern
1
2
=
1
6
1
×
1
+
1
×
2
×
1
+
1
1
2
+
2
2
=
1
6
2
×
2
+
1
×
2
×
2
+
1
1
2
+
2
2
+
3
2
=
1
6
3
×
3
+
1
×
2
×
3
+
1
1
2
+
2
2
+
3
2
+
4
2
=
1
6
4
×
4
+
1
×
2
×
4
+
1
and find the values of each of the following:
(i) 1
2
+ 2
2
+ 3
2
+ 4
2
+ ... + 10
2
(ii) 5
2
+ 6
2
+ 7
2
+ 8
2
+ 9
2
+ 10
2
+ 11
2
+ 12
2
Q.
Find the value of:
(1)
(2)
(3)
(4)
(5)