MathDB
Problems
Contests
Undergraduate contests
Putnam
1950 Putnam
A2
A2
Part of
1950 Putnam
Problems
(1)
Putnam 1950 A2
Source:
5/24/2022
Answer both (i) and (ii). Test for convergence the series(i)
1
log
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2
!
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1
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3
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1
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4
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1
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n
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\frac 1{\log (2!)} + \frac 1{\log (3!)} + \frac 1{\log (4!)} + \cdots + \frac 1{\log (n!)} +\cdots
lo
g
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2
!)
1
+
lo
g
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3
!)
1
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lo
g
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4
!)
1
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⋯
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lo
g
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n
!)
1
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⋯
(ii)
1
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1
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1
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3
n
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⋯
\frac 13 + \frac 1{3\sqrt3} + \frac 1{3\sqrt3 \sqrt[3]3} + \cdots + \frac 1{3\sqrt3 \sqrt[3]3 \cdots \sqrt[n]3} + \cdots
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3
3
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3
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3
3
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n
3
1
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⋯
Putnam