MathDB
Problems
Contests
Undergraduate contests
Putnam
1950 Putnam
A2
Putnam 1950 A2
Putnam 1950 A2
Source:
May 24, 2022
Putnam
Problem Statement
Answer both (i) and (ii). Test for convergence the series(i)
1
log
(
2
!
)
+
1
log
(
3
!
)
+
1
log
(
4
!
)
+
⋯
+
1
log
(
n
!
)
+
⋯
\frac 1{\log (2!)} + \frac 1{\log (3!)} + \frac 1{\log (4!)} + \cdots + \frac 1{\log (n!)} +\cdots
lo
g
(
2
!)
1
+
lo
g
(
3
!)
1
+
lo
g
(
4
!)
1
+
⋯
+
lo
g
(
n
!)
1
+
⋯
(ii)
1
3
+
1
3
3
+
1
3
3
3
3
+
⋯
+
1
3
3
3
3
⋯
3
n
+
⋯
\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
3
1
+
3
3
1
+
3
3
3
3
1
+
⋯
+
3
3
3
3
⋯
n
3
1
+
⋯
Back to Problems
View on AoPS