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CGPET 2014 Solved Paper
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Section:
Mathematics
© examsiri.com
Question :
135 of 150
Marks:
+1
,
-0
The sum of
n
terms of the series
1
+
5
+
12
+
22
+
35
+
.
.
.
is
‌
n
2
(
n
+
1
)
8
‌
n
2
(
n
+
1
)
6
‌
n
2
(
n
+
1
)
2
None of these
Validate
Solution:
- Let
‌
S
n
=
1
+
5
+
12
+
22
+
35
+
.
.
.
+
T
n
‌
S
n
=
1
+
5
+
12
+
22
+
.
.
.
+
T
n
‌
0
=
1
+
4
+
7
+
10
+
13
+
.
.
.
−
T
n
‌
⇒
T
n
=
1
+
4
+
7
+
10
+
13
+
.
.
.
+
n
‌
terms
‌
This is an arithmetic series whose first term a is 1 and common difference
d
is 3 .
∴
‌
T
n
=
‌
n
2
[
2
×
1
+
(
n
−
1
)
3
]
⇒
T
n
=
‌
n
2
[
2
+
3
n
−
3
]
‌
=
‌
n
2
[
3
n
−
1
]
‌
=
‌
1
2
[
3
n
2
−
n
]
S
n
‌
=
Σ
T
n
‌
=
‌
1
2
[
Σ
(
3
n
2
−
n
)
]
‌
=
‌
1
2
[
3
Σ
n
2
−
Σ
n
]
‌
=
‌
1
2
[
‌
3
n
(
n
+
1
)
(
2
n
+
1
)
6
−
‌
n
(
n
+
1
)
2
]
‌
=
‌
n
(
n
+
1
)
2
[
‌
2
n
+
1
2
−
‌
1
2
]
‌
=
‌
n
(
n
+
1
)
2
[
‌
2
n
2
]
=
‌
n
2
(
n
+
1
)
2
© examsiri.com
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