Question Number 186468 by aba last updated on 04/Feb/23

Simplify ((1^2 ∙2!+2^2 ∙3!+3^2 ∙4!+∙∙∙+n^2 (n+1)!−2)/((n+1)!)) to n^2 +n−2

Answered by SEKRET last updated on 07/Feb/23

1^2 ∙2=2 2^2 ∙3!=4! 3^2 ∙4!=2∙5!−4! 4^2 ∙5!=3∙6!−2∙5! 5^2 ∙6!=4∙7!-3∙6! ....... ............ n^2 (n+1)!=(n−1)∙(n+2)! −(n−2)∙(n+1)! (+) all 2+(n−1)∙(n+2)! ((2+(n−1)∙(n+2)! −2)/((n+1)!))=(((n−1)∙(n+2)(n+1)!)/((n+1)!)) = (n−1)(n+2)=n^2 +n−2 ABDULAZIZ ABDUVALIYEV

Commented byaba last updated on 11/Feb/23

thank a lot💓