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Manipal Entrance Test 2013 Math Paper
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© examsnet.com
Question : 2
Total: 80
The sum to n terms of the series:
1
1
+
1
2
+
1
4
+
2
1
+
2
2
+
2
4
+
3
1
+
3
2
+
3
4
+
.
.
.
.
.
.
is
n
2
+
1
2
(
n
2
+
n
+
1
)
n
2
+
n
(
n
2
+
n
+
1
)
n
2
+
n
2
(
n
2
+
n
+
1
)
None of these
Validate
Solution:
Let
T
r
be the r
th
term of the given series.
Then,
T
r
=
r
1
+
r
2
+
r
4
r
=
1
,
2
,
3
,
.
.
.
,
n
=
r
(
r
2
+
r
+
1
)
(
r
2
−
r
+
1
)
=
1
2
[
1
r
2
−
r
+
1
−
1
r
2
+
r
+
1
]
∴ Sum of the series
=
n
∑
r
=
1
T
r
=
1
2
n
∑
r
=
1
(
1
r
2
−
r
+
1
−
1
r
2
+
r
+
1
)
}
=
1
2
{
(
1
−
1
3
)
+
(
1
3
−
1
7
)
+
(
1
7
−
1
13
)
+
.
.
.
.
.
+
(
1
n
2
−
n
+
1
−
1
n
2
+
n
+
1
)
}
=
1
2
{
1
−
1
n
2
+
n
+
1
}
=
n
2
+
n
2
(
n
2
+
n
+
1
)
© examsnet.com
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