Question Number 222466 by klipto last updated on 27/Jun/25
$$\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}.\: \\ $$
Commented by klipto last updated on 27/Jun/25
Commented by Frix last updated on 28/Jun/25
$$\mathrm{It}'\mathrm{s}\:\mathrm{not}\:\mathrm{unique}. \\ $$$$\mathrm{Using}\:\mathrm{polynomials}\:\mathrm{we}\:\mathrm{get} \\ $$$${a}_{{n}} =\frac{\mathrm{1}}{{b}_{{n}} }=\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right)} \\ $$$$\mathrm{or} \\ $$$${a}_{{n}} =\frac{\mathrm{17}{n}^{\mathrm{4}} }{\mathrm{8064}}−\frac{\mathrm{125}{n}^{\mathrm{3}} }{\mathrm{4032}}+\frac{\mathrm{759}{x}^{\mathrm{2}} }{\mathrm{4480}}−\frac{\mathrm{8357}{x}}{\mathrm{20160}}+\frac{\mathrm{2011}}{\mathrm{5040}} \\ $$$$…\mathrm{zillions}\:\mathrm{of}\:\mathrm{other}\:\mathrm{solutions}… \\ $$
Commented by klipto last updated on 28/Jun/25
$$\mathrm{lol}…\:\mathrm{a}\:\mathrm{solution}\:\mathrm{process}\:\mathrm{frix} \\ $$
Commented by klipto last updated on 28/Jun/25
$$\mathrm{yeah}\:\mathrm{exactly}\:\mathrm{thanks},\boldsymbol{\mathrm{youve}}\:\boldsymbol{\mathrm{got}}\:\boldsymbol{\mathrm{some}}\:\boldsymbol{\mathrm{crazy}} \\ $$$$\boldsymbol{\mathrm{pdfs}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{advance}}\:\boldsymbol{\mathrm{math}}?\:\left(\mathrm{name}\right) \\ $$