On Apr 25, 2:50 pm, "Simon Johan" <si...@johan.invalid> wrote:
"Robert Israel" <isr...@math.MyUniversitysInitials.ca> wrote in message
news:rbisrael.20080425203654$4571@news.ks.uiuc.edu...
"Simon Johan" <si...@johan.invalid> writes:
I'm trying to understand an equation which I have seen in two books. I
states the following inequality: n/HarmonicNumber(n) <= n/log n <=
n/log2
n
where the n'th harmonic number is the sum from i = 1 to n of 1/i and
log
is
the natural logarithm and log2 is the logarithm with base 2.
n/HarmonicNumber(n) <= n/log(n) since the n'th harmonic number is
greater
than log(n) for every n, but the last part I don't get.
Good, because it's false. Try n = 5.
Thanks, that's reassuring, but there must be something wrong. Maybe you
could have a look at the bottom of page 4 in this
articlehttp://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890017081_1989...
It states: sum from i = 1 to N of 1/i >= log2(N) which should be equal to
the inequality above here. Am I messing up the notation?
Either the author is ignoring constant factors, or he made a mistake.
