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Putnam
1975 Putnam
B5
B5
Part of
1975 Putnam
Problems
(1)
Putnam 1975 B5
Source: Putnam 1975
2/17/2022
Define
f
0
(
x
)
=
e
x
f_{0}(x)=e^x
f
0
(
x
)
=
e
x
and
f
n
+
1
(
x
)
=
x
f
n
′
(
x
)
f_{n+1}(x)=x f_{n}'(x)
f
n
+
1
(
x
)
=
x
f
n
′
(
x
)
. Show that
∑
n
=
0
∞
f
n
(
1
)
n
!
=
e
e
\sum_{n=0}^{\infty} \frac{f_{n}(1)}{n!}=e^e
∑
n
=
0
∞
n
!
f
n
(
1
)
=
e
e
.
Putnam
function
Convergence