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Byju's Answer
Standard XII
Mathematics
Proof by mathematical induction
Evaluate li...
Question
Evaluate
lim
n
→
∞
(
1
n
2
+
1
+
1
n
2
+
2
+
1
n
2
+
3
+
.
.
.
+
n
n
2
+
n
)
Open in App
Solution
lim
n
→
∞
(
1
n
2
+
1
+
1
n
2
+
2
+
1
n
2
+
3
+
.
.
.
.
.
.
+
n
n
2
+
n
)
Now dividing both numerator and denominator by
n
2
lim
n
→
∞
⎛
⎜
⎝
1
n
2
1
+
1
n
2
+
1
n
2
1
+
2
n
2
+
1
n
2
1
+
3
n
2
+
.
.
.
.
.
.
+
1
n
2
1
+
1
n
⎞
⎟
⎠
=
0
1
+
0
1
+
0
1
.
.
.
.
.
.
.
.
0
1
=
0
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0
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