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Re: Harmonic numbers

From: Jaroslav Hajek
Subject: Re: Harmonic numbers
Date: Fri, 26 Feb 2010 07:15:06 +0100

On Thu, Feb 25, 2010 at 11:43 PM, Iliopoulos Vasileios
<address@hidden> wrote:
> Hi All,
> I am beginner in GNU Octave. I would like to ask you how to compute
> in Octave the folloing expresssion
> \sum_{j=1}^{n}harmonic(j)
> Where harmonic(j):=\sum_{i=1}^{j}1/i
> Thanks

You can generate the first n harmonic numbers by

h = cumsum (1 ./ (1:n));

And sum them using sum:

x = sum (h);

Or you can figure out the formula that holds for harmonic numbers:
sum (h(1:n)) = (n+1)*h(n) - n,
and use that to compute more accurately.

RNDr. Jaroslav Hajek, PhD
computing expert & GNU Octave developer
Aeronautical Research and Test Institute (VZLU)
Prague, Czech Republic

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