Çözüldü Dizi Karakteri İncelemesi

https://i.ibb.co/C2mScH7/dizi2.jpg
https://www.facebook.com/photo.php?fbid=3784167978291198&set=gm.3520791011269572&type=3&theater

D'Alembert Oran Testi uygulanırsa;
lim (n → ∞) [ 26^(n + 1) ]·{ [ (n + 1)! ]^3 }·(3n!) / { (26^n)·[ 3(n + 1) ]!·[ (n!)^3 ] } =
lim (n → ∞) 26·[ (n + 1)^3 ] / [ 3(n + 1)(3n + 2)(3n + 3) = 26 / 27 < 1 olduğundan seri yakınsak (convergent)

Sonucun WolframAlpha Kontrolları:

https://i.ibb.co/mv7dSS5/dizi2-WA2.png
https://www.wolframalpha.com/input/?i=sum (26^n)((n!)^3)/(3n)!, n=1 to infinity


https://i.ibb.co/QnTK7qY/dizi2-WA1.png
https://www.wolframalpha.com/input/?i=lim ((26^(n+1)((n+1)!)^3))(3n)!/((26^n)((n!)^3)((3(n+1))!))as n goes to infinity

Faktöriyelli ifadenin sadeleşmiş halinin kontrolu:

https://i.ibb.co/J7M1cbC/dizi2-WA.png
https://www.wolframalpha.com/input/?i=((n!)^3/(3n)!)((3(n+1))!/(((n+1)!)^3))-(3(n+1)(3n+2)(3n+1))/((n+1)^3)=
(Result: 0 yani iki ifade birbirine eşit)