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This is obviously a really good signing. The Twins are largely a product of their pitching depth, and with Francisco Liriano leaving for the Dominican Republic, the Twins need a quality outfielder for the three outfield positions, with Torii Hunter and Denard Span set to be the primary outfielders and Michael Cuddyer sliding over to center. Hunter, Span and Cuddyer account for four of the five starting spots in the order.
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Hunter and Span each have to be joined at some point by one of three free agents: Lyle Overbay, Mark DeRosa and Josh Willingham. Moss would obviously join the Twins outfield mix, giving the team some much-needed speed. He hit 22 home runs this year, but so did the White Sox, as he led the American League in home runs hit by a left-handed hitter. He was also a much-improved defender in left field, with a.986 fielding percentage.
Moss would give the Twins a legitimate left-handed power threat, which would help balance out what was a right-handed power-oriented lineup last year. The Twins’ first-base platoon of Rene Rivera and Trevor Plouffe struggled.
The team has some other needs, though. After losing Denard Span, it would be helpful if the team could get some more from its young outfielders. Michael https://startpointsudan.com/wp-content/uploads/2022/06/conssch.pdf
Apr 7, 2020
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the result of a geometric progression
The solution to part (b) gives the formula
Note that this also gives the logarithm of 1! to be (assuming is positive)
The final part is a geometric progression with ratio
And so its logarithm is
Note that in this case it is only necessary to know that is positive. This is because the case of a negative is the same as the case of with the negatives signs changed.
Part (c) asks for the quantity
This can be readily calculated with elementary means. For part (d), note that the logarithm of a product of two positive terms is given by the sum of the logarithms.
And for (e) note that implies that
This is equivalent to
thus
Using the definitions of the harmonic numbers and the property it can be shown that
and so
The final part (f) allows for the substitution, and so
We conclude that the harmonic numbers satisfy the recurrence relation
where is the floor function. Thus the harmonic numbers satisfy the recurrence relation
and so
and consequently
This proves the harmonic series is divergent.
References
may be used as a reference for special cases, and specialized information can be found in the references.
and The Wolfram MathWorld page on harmonic numbers
.
Category:Logarithms
Category:Articles containing proofs
Category:Analytic number theoryQ:
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