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AIEEE 2003 Math Solved Paper
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© examsnet.com
Question : 59
Total: 66
lim
n
→
∞
1
+
2
4
+
3
4
+
.
.
.
+
n
4
n
5
−
lim
n
→
∞
1
+
2
3
+
3
3
+
.
.
.
+
n
3
n
5
1
5
1
30
zero
1
4
Validate
Solution:
The given expression can be written as
lim
n
→
∞
1
n
n
∑
r
=
1
(
r
n
)
4
−
lim
n
→
∞
1
n
.
lim
n
→
∞
1
n
(
r
n
)
3
=
1
∫
0
x
4
dx
−
lim
n
→
∞
1
n
×
1
∫
0
x
3
dx
=
[
x
5
5
]
0
1
−
0
=
1
5
© examsnet.com
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