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Manipal Entrance Test 2013 Math Paper
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© examsnet.com
Question : 1
Total: 80
The least positive integer n, for which
n
!
<
(
n
+
1
2
)
n
holds, is
1
2
3
4
Validate
Solution:
For
n
=
1
,
1
!
<
(
1
)
1
that is, 1 < 1 is not true
For
n
=
2
,
2
!
<
(
3
2
)
1
that is,
2
<
9
4
is true,
By induction,
n
!
<
(
n
+
1
2
)
n
∀
n
∈
N
for
n
>
2
.
∴ least
n
=
2.
© examsnet.com
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