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IMC
1997 IMC
3
Sum convergence
Sum convergence
Source: IMC 1997 day 2 problem 3
October 19, 2005
trigonometry
logarithms
floor function
function
integration
absolute value
complex numbers
Problem Statement
Show that
∑
n
=
1
∞
(
−
1
)
n
−
1
sin
(
log
n
)
n
α
\sum^{\infty}_{n=1}\frac{(-1)^{n-1}\sin(\log n)}{n^\alpha}
∑
n
=
1
∞
n
α
(
−
1
)
n
−
1
s
i
n
(
l
o
g
n
)
converges iff
α
>
0
\alpha>0
α
>
0
.
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