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Putnam
1951 Putnam
A7
A7
Part of
1951 Putnam
Problems
(1)
Putnam 1951 A7
Source:
5/25/2022
Show that if the series
a
1
+
a
2
+
a
3
+
⋯
+
a
n
+
⋯
a_1 + a_2 + a_3 + \cdots + a_n + \cdots
a
1
+
a
2
+
a
3
+
⋯
+
a
n
+
⋯
converges, then the series
a
1
+
a
2
/
2
+
a
3
/
3
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⋯
+
a
n
/
n
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⋯
a_1 + a_2 / 2 + a_3 / 3 + \cdots + a_n / n + \cdots
a
1
+
a
2
/2
+
a
3
/3
+
⋯
+
a
n
/
n
+
⋯
converges also.
Putnam