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Putnam
1941 Putnam
B2
B2
Part of
1941 Putnam
Problems
(1)
Putnam 1941 B2
Source: Putnam 1941
2/23/2022
Find (i)
lim
n
→
∞
∑
i
=
1
n
1
n
2
+
i
2
\lim_{n\to \infty} \sum_{i=1}^{n} \frac{1}{\sqrt{n^2 +i^{2}}}
lim
n
→
∞
∑
i
=
1
n
n
2
+
i
2
1
. (ii)
lim
n
→
∞
∑
i
=
1
n
1
n
2
+
i
\lim_{n\to \infty} \sum_{i=1}^{n} \frac{1}{\sqrt{n^2 +i}}
lim
n
→
∞
∑
i
=
1
n
n
2
+
i
1
. (iii)
lim
n
→
∞
∑
i
=
1
n
2
1
n
2
+
i
\lim_{n\to \infty} \sum_{i=1}^{n^{2}} \frac{1}{\sqrt{n^2 +i}}
lim
n
→
∞
∑
i
=
1
n
2
n
2
+
i
1
.
Putnam
Convergence
series