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Simplify-1-2-2-2-2-3-3-2-4-n-2-n-1-2-n-1-to-n-2-n-2-

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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
Simplify12⋅2!+22⋅3!+32⋅4!+⋅⋅⋅+n2(n+1)!−2(n+1)!ton2+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
12⋅2=222⋅3!=4!32⋅4!=2⋅5!−4!42⋅5!=3⋅6!−2⋅5!52⋅6!=4⋅7!−3⋅6!…….…………n2(n+1)!=(n−1)⋅(n+2)!−(n−2)⋅(n+1)!(+)all2+(n−1)⋅(n+2)!2+(n−1)⋅(n+2)!−2(n+1)!=(n−1)⋅(n+2)(n+1)!(n+1)!=(n−1)(n+2)=n2+n−2ABDULAZIZABDUVALIYEV
Commented by aba last updated on 11/Feb/23
thank a lot��

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