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The value of _ n 1^3+2^3+3^3+ +n^3 (n^2+1)^2 is
MATHEMATICS · Single correct · ISC · Mathematics · Algebra · Algebra
Problem
The value of
lim
n
→
∞
1
3
+
2
3
+
3
3
+
⋯
+
n
3
(
n
2
+
1
)
2
\lim_{n\to\infty}\frac{1^3+2^3+3^3+\dots+n^3}{(n^2+1)^2}
n
→
∞
lim
(
n
2
+
1
)
2
1
3
+
2
3
+
3
3
+
⋯
+
n
3
is (1)
1
4
\frac14
4
1
(2)
1
2
\frac12
2
1
(3)
2
2
2\sqrt2
2
2
(4) None of these
Related theory
Limits
Special Series
Special sums
Algebra
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