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Putnam
1992 Putnam
A2
A2
Part of
1992 Putnam
Problems
(1)
Putnam 1992 A2
Source: Putnam 1992
7/18/2022
Define
C
(
α
)
C(\alpha)
C
(
α
)
to be the coefficient of
x
1992
x^{1992}
x
1992
in the power series about
x
=
0
x = 0
x
=
0
of
(
1
+
x
)
α
(1 + x)^{\alpha}
(
1
+
x
)
α
. Evaluate
∫
0
1
(
C
(
−
y
−
1
)
∑
k
=
1
1992
1
y
+
k
)
d
y
.
\int_{0}^{1} \left( C(-y-1) \sum_{k=1}^{1992} \frac{1}{y+k} \right)\, dy.
∫
0
1
(
C
(
−
y
−
1
)
k
=
1
∑
1992
y
+
k
1
)
d
y
.
Putnam
Integral
power series