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Could you help me here?

Prove elementarily that $L_n$ is strictly decreasing


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May
10
 awarded  Nice Question
May
9
 revised Evaluation of a triple sum does not finish in reasonable time
deleted 11 characters in body
May
8
 accepted Evaluation of a triple sum does not finish in reasonable time
May
8
 asked Evaluation of a triple sum does not finish in reasonable time
Apr
25
 awarded  Commentator
Apr
25
 comment The proper way to write the input for a certain series
Maybe it's time people from Wolfram improve their software ;)
Apr
25
 comment The proper way to write the input for a certain series
@DanielLichtblau I'm somewhat surprised to see Mathematics v8.0 is not able to provide with a correct answer. I was thinking my input is not correct.
Apr
25
 comment The proper way to write the input for a certain series
@Szabolcs I use v8.0 here.
Apr
25
 comment The proper way to write the input for a certain series
By the alternating series test it's clear the series converges, but it seems the convergence is very slow.
Apr
25
 asked The proper way to write the input for a certain series
Feb
28
 revised Why is the output of my limit expression an interval?
edited title
Feb
28
 awarded  Student
Feb
27
 comment Why is the output of my limit expression an interval?
thank you for your explanations!
Feb
27
 accepted Why is the output of my limit expression an interval?
Feb
27
 awarded  Editor
Feb
27
 revised Why is the output of my limit expression an interval?
added 10 characters in body
Feb
27
 asked Why is the output of my limit expression an interval?
Feb
20
 awarded  Scholar
Feb
20
 awarded  Supporter
Feb
20
 accepted No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
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