Exercise:
Indaga empiricamente con Excel come si comportano queste successioni disegnando in particolare il loro grafico: footnoteLa funzione per la potenza su Excel è textitPOWab oppure l'accento circonflesso ^ quella per il fattoriale textitFACTn abclist abc displaystyle anfracn^+nnn+qquad ngeq abc displaystyle bnleft+fracnright^nqquad ngeq abc displaystyle cnfracn^n+/n! e^nqquad ngeq abclist

Solution:
La prima sembra stabilizzarsi attorno a . center tikzpicturescale. axis axis linesmiddle enlargelimitsfalse axis line styleshorten -pt shorten -pt xlabel styleanchorwest atticklabel* cs:. xshiftpt ylabel styleanchorsouth atticklabel* cs:. yshiftpt xlabel n ylabel an xmin xmax ymin ymax ytick--... xtick... minor x tick num minor y tick num minor grid styleblack! major grid styleblack! grid yminorgrids xminorgrids major tick lengthpt every tick/.style semithick addplot only marksmark size.ptblack domain: samples x^+*x/*x*x+; drawfillwhite . rectangle ; draw . node right displaystyle anfracn^+nnn+; axis tikzpicture center La seconda sembra stabilizzarsi attorno a . center tikzpicturescale. axis axis linesmiddle enlargelimitsfalse axis line styleshorten -pt shorten -pt xlabel styleanchorwest atticklabel* cs:. xshiftpt ylabel styleanchorsouth atticklabel* cs:. yshiftpt xlabel n ylabel bn xmin xmax ymin ymax ytick... xtick... minor x tick num minor y tick num minor grid styleblack! major grid styleblack! grid yminorgrids xminorgrids major tick lengthpt every tick/.style semithick addplot only marksmark size.ptblack domain: samples +/x^x; drawfillwhite . rectangle ; draw . node right displaystyle bnleft+fracnright^n; axis tikzpicture center La terza sembra stabilizzarsi attorno a .. La realtà è che si stabilizza attorno a fracsqrtpi. center tikzpicturescale. axis axis linesmiddle enlargelimitsfalse axis line styleshorten -pt shorten -pt xlabel styleanchorwest atticklabel* cs:. xshiftpt ylabel styleanchorsouth atticklabel* cs:. yshiftpt xlabel n ylabel cn xmin xmax ymin ymax ytick... xtick... minor x tick num minor y tick num minor grid styleblack! major grid styleblack! grid yminorgrids xminorgrids major tick lengthpt every tick/.style semithick addplot only marksmark size.ptblack domain: samples powxx*sqrtx/expx*factorialx; drawfillwhite . rectangle ; draw . node right displaystyle cnfracn^n+/n! e^n; axis tikzpicture center