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Putnam
1982 Putnam
A2
converge of infinite faulhaber sum
converge of infinite faulhaber sum
Source: Putnam 1982 A2
September 19, 2021
Summation
real analysis
algebra
Problem Statement
For positive real
x
x
x
, let
B
n
(
x
)
=
1
x
+
2
x
+
…
+
n
x
.
B_n(x)=1^x+2^x+\ldots+n^x.
B
n
(
x
)
=
1
x
+
2
x
+
…
+
n
x
.
Prove or disprove the convergence of
∑
n
=
2
∞
B
n
(
log
n
2
)
(
n
log
2
n
)
2
.
\sum_{n=2}^\infty\frac{B_n(\log_n2)}{(n\log_2n)^2}.
n
=
2
∑
∞
(
n
lo
g
2
n
)
2
B
n
(
lo
g
n
2
)
.
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