HP50g -> computing whether or not (mathematical) series converge, and, if so, which value to?
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From: Merciadri Luca on 1 Jun 2010 12:07 -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 mjc <mjcohen(a)acm.org> writes: > On May 30, 1:13 pm, supergems <simone.cer...(a)gmail.com> wrote: >> On 29 Mag, 14:25, Merciadri Luca <Luca.Mercia...(a)student.ulg.ac.be> >> wrote: >> >> >> >> > -----BEGIN PGP SIGNED MESSAGE----- >> > Hash: SHA1 >> >> > Hi, >> >> > It is sometimes interesting not to have to use Abel's theorem, or >> > Quotient's and Root's criteria, but to know, electronically, if a >> > serie (of function, or not), converge, and, if so, the value to which >> > it converges. Can it be done with the HP 50g? Implementing these >> > methods on it should be straightforward, as it uses >> >> > * basic calculus notions: limits, comparison criteria; >> > * basic algebra notions: decomposition into simple els., solving >> > * (in)equations with absolute values (for absolute convergence), >> >> > and all these features are already implemented on the HP >> > 50g. Evidently, finding the value to which a serie converges is not >> > always feasible, but when it is feasible (say for trivial series, such >> > as those which simply need indices modifications, and decomposition in >> > simple els.) for an human, the HP50g should do it. >> >> > This might be very useful, because such series (of function or not, >> > simple numeric series) sometimes arise in practice, say e.g. from Taylor's >> > infinite developments. >> >> > Thanks. >> > - -- >> > Merciadri Luca >> > Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/ >> > - -- >> >> > When I was born, I was so surprised I didn't talk for a year and a >> > half. (Gracie Allen) >> > -----BEGIN PGP SIGNATURE----- >> > Version: GnuPG v1.4.9 (GNU/Linux) >> > Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> >> >> > iEYEARECAAYFAkwBB9EACgkQM0LLzLt8MhwZHgCgpukck/FW8NYRbIQCgDSwW5ds >> > /vAAnRgz7d1rTRIPA1b3BmGv1oUJWYB3 >> > =1Y8k >> > -----END PGP SIGNATURE----- >> >> Hi Luca, you read >> >> Sequences, Series and Limits Marathonhttp://www.hpcalc.org/details.php?id=5290 >> >> and all marathon bookshttp://www.hpcalc.org/search.php?query=marathon >> >> supergems > > You might also try Aitken extrapolation (and it's cousin Steffenson > (sp?)). Thanks. I'll have a look at it too. - -- Merciadri Luca See http://www.student.montefiore.ulg.ac.be/~merciadri/ - -- Live as if you were to die tomorrow; learn as if you were to live forever. (Mahatma Gandhi) -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkwFMD4ACgkQM0LLzLt8MhyxsACfRlSKycTNxcaE/2JrnQf4MDTI 5a0An0VXkKFhbt7ecJIBb52hT8Xnb77A =BmYn -----END PGP SIGNATURE-----
From: Merciadri Luca on 1 Jun 2010 12:07
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 supergems <simone.cerica(a)gmail.com> writes: > On 29 Mag, 14:25, Merciadri Luca <Luca.Mercia...(a)student.ulg.ac.be> > wrote: >> -----BEGIN PGP SIGNED MESSAGE----- >> Hash: SHA1 >> >> Hi, >> >> It is sometimes interesting not to have to use Abel's theorem, or >> Quotient's and Root's criteria, but to know, electronically, if a >> serie (of function, or not), converge, and, if so, the value to which >> it converges. Can it be done with the HP 50g? Implementing these >> methods on it should be straightforward, as it uses >> >> * basic calculus notions: limits, comparison criteria; >> * basic algebra notions: decomposition into simple els., solving >> * (in)equations with absolute values (for absolute convergence), >> >> and all these features are already implemented on the HP >> 50g. Evidently, finding the value to which a serie converges is not >> always feasible, but when it is feasible (say for trivial series, such >> as those which simply need indices modifications, and decomposition in >> simple els.) for an human, the HP50g should do it. >> >> This might be very useful, because such series (of function or not, >> simple numeric series) sometimes arise in practice, say e.g. from Taylor's >> infinite developments. >> >> Thanks. >> - -- >> Merciadri Luca >> Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/ >> - -- >> >> When I was born, I was so surprised I didn't talk for a year and a >> half. (Gracie Allen) >> -----BEGIN PGP SIGNATURE----- >> Version: GnuPG v1.4.9 (GNU/Linux) >> Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> >> >> iEYEARECAAYFAkwBB9EACgkQM0LLzLt8MhwZHgCgpukck/FW8NYRbIQCgDSwW5ds >> /vAAnRgz7d1rTRIPA1b3BmGv1oUJWYB3 >> =1Y8k >> -----END PGP SIGNATURE----- > > Hi Luca, you read > > Sequences, Series and Limits Marathon > http://www.hpcalc.org/details.php?id=5290 > > and all marathon books > http://www.hpcalc.org/search.php?query=marathon Thanks for pointing them out. I had not thought about hpcalc.org for this. Thanks. - -- Merciadri Luca See http://www.student.montefiore.ulg.ac.be/~merciadri/ - -- When making your choices in life, do not forget to live. (Samuel Johnson) -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkwFMFMACgkQM0LLzLt8Mhy6BgCfQTdrz7/rrLzFdn0furGnobX2 p4AAnRxL2f09zHs3fi5woHmWRyUPNdU7 =CFaq -----END PGP SIGNATURE----- |