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Mathematics
Mathematics
Problem
The value of
lim
n
→
∞
[
n
n
2
+
n
n
2
+
1
+
n
n
2
+
4
+
⋯
+
n
2
n
2
−
2
n
+
1
]
\lim_{n \to \infty} \left[ \frac{n}{n^2} + \frac{n}{n^2+1} + \frac{n}{n^2+4} + \dots + \frac{n}{2n^2-2n+1} \right]
lim
n
→
∞
[
n
2
n
+
n
2
+
1
n
+
n
2
+
4
n
+
⋯
+
2
n
2
−
2
n
+
1
n
]
is (A)
π
4
\frac{\pi}{4}
4
π
(B)
π
2
\frac{\pi}{2}
2
π
(C)
π
3
\frac{\pi}{3}
3
π
(D) None of these
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