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Standard XII
Mathematics
Algebra of Limits
Question
lim
n
→
∞
1
2
+
2
2
+
3
2
+
.
.
.
.
+
n
2
n
3
is equal to
1
/
2
0
1
1
/
3
A
1
/
2
B
1
C
1
/
3
D
0
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Solution
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Solution
lim
x
→
∞
1
2
+
2
2
+
−
−
−
n
2
n
3
we know that
1
2
+
2
2
+
−
−
−
n
2
=
n
(
n
+
1
)
(
2
n
+
1
)
6
=
lim
x
→
∞
n
(
n
+
1
)
(
2
n
+
1
)
6
n
3
=
lim
x
→
∞
(
n
+
1
)
(
2
n
+
1
)
6
n
2
=
lim
x
→
∞
2
n
2
+
3
n
+
1
6
n
2
Apply L-Hospital rule twice.
=
lim
x
→
∞
4
n
+
3
12
n
=
4
12
=
1
3
C is correct.
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