连分数 $1+1/(2+1/(3+1/(4+1/(5+\cdots+))))$
(以下使用 Calculator 计算)
>> setprecision(200)
in> setprecision(200)
Now the precision is: 200
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>> continued_fraction(1,2,...,100)
in> continued_fraction(1,2,...,100)
out> 210628326606030925509504995396115751215082237173770949560136689651065020446811215535403721603460152269102594085067245222090841983806373539433329769060736986251|146971108555054591263734471078160507352050045572198741030186489794108431298591736983812285328810821610957278981960240168856854819813194627616076643581220741550
Expression:
1+1/(2+1/(3+1/(4+1/(5+1/(6+1/(7+1/(8+1/(9+1/(10+1/(11+1/(12+1/(13+1/(14+1/(15+1/(16+1/(17+1/(18+1/(19+1/(20+1/(21+1/(22+1/(23+1/(24+1/(25+1/(26+1/(27+1/(28+1/(29+1/(30+1/(31+1/(32+1/(33+1/(34+1/(35+1/(36+1/(37+1/(38+1/(39+1/(40+1/(41+1/(42+1/(43+1/(44+1/(45+1/(46+1/(47+1/(48+1/(49+1/(50+1/(51+1/(52+1/(53+1/(54+1/(55+1/(56+1/(57+1/(58+1/(59+1/(60+1/(61+1/(62+1/(63+1/(64+1/(65+1/(66+1/(67+1/(68+1/(69+1/(70+1/(71+1/(72+1/(73+1/(74+1/(75+1/(76+1/(77+1/(78+1/(79+1/(80+1/(81+1/(82+1/(83+1/(84+1/(85+1/(86+1/(87+1/(88+1/(89+1/(90+1/(91+1/(92+1/(93+1/(94+1/(95+1/(96+1/(97+1/(98+1/(99+1/(100)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
TeX Code:
1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5+\frac{1}{6+\frac{1}{7+\frac{1}{8+\frac{1}{9+\frac{1}{10+\frac{1}{11+\frac{1}{12+\frac{1}{13+\frac{1}{14+\frac{1}{15+\frac{1}{16+\frac{1}{17+\frac{1}{18+\frac{1}{19+\frac{1}{20+\frac{1}{21+\frac{1}{22+\frac{1}{23+\frac{1}{24+\frac{1}{25+\frac{1}{26+\frac{1}{27+\frac{1}{28+\frac{1}{29+\frac{1}{30+\frac{1}{31+\frac{1}{32+\frac{1}{33+\frac{1}{34+\frac{1}{35+\frac{1}{36+\frac{1}{37+\frac{1}{38+\frac{1}{39+\frac{1}{40+\frac{1}{41+\frac{1}{42+\frac{1}{43+\frac{1}{44+\frac{1}{45+\frac{1}{46+\frac{1}{47+\frac{1}{48+\frac{1}{49+\frac{1}{50+\frac{1}{51+\frac{1}{52+\frac{1}{53+\frac{1}{54+\frac{1}{55+\frac{1}{56+\frac{1}{57+\frac{1}{58+\frac{1}{59+\frac{1}{60+\frac{1}{61+\frac{1}{62+\frac{1}{63+\frac{1}{64+\frac{1}{65+\frac{1}{66+\frac{1}{67+\frac{1}{68+\frac{1}{69+\frac{1}{70+\frac{1}{71+\frac{1}{72+\frac{1}{73+\frac{1}{74+\frac{1}{75+\frac{1}{76+\frac{1}{77+\frac{1}{78+\frac{1}{79+\frac{1}{80+\frac{1}{81+\frac{1}{82+\frac{1}{83+\frac{1}{84+\frac{1}{85+\frac{1}{86+\frac{1}{87+\frac{1}{88+\frac{1}{89+\frac{1}{90+\frac{1}{91+\frac{1}{92+\frac{1}{93+\frac{1}{94+\frac{1}{95+\frac{1}{96+\frac{1}{97+\frac{1}{98+\frac{1}{99+\frac{1}{100}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
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>> 210628326606030925509504995396115751215082237173770949560136689651065020446811215535403721603460152269102594085067245222090841983806373539433329769060736986251/146971108555054591263734471078160507352050045572198741030186489794108431298591736983812285328810821610957278981960240168856854819813194627616076643581220741550
in> 210628326606030925509504995396115751215082237173770949560136689651065020446811215535403721603460152269102594085067245222090841983806373539433329769060736986251/146971108555054591263734471078160507352050045572198741030186489794108431298591736983812285328810821610957278981960240168856854819813194627616076643581220741550
out> 1.43312742672231175831718345577599182043151276790598052343442863639430918325417290013650372643578611465950013404308853642953017708273894637360407321952533635247368315637151340965862626563444808561719787
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其他参考资料
https://math.stackexchange.com/questions/69519/closed-form-for-a-pair-of-continued-fractions