求数列an=(2n-1)(2n+1)(2n+3)前n项的和 求和:1*1!+2*2!+3*3!+...+n*n!

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求数列an=(2n-1)(2n+1)(2n+3)前n项的和 求和:1*1!+2*2!+3*3!+...+n*n!

求数列an=(2n-1)(2n+1)(2n+3)前n项的和 求和:1*1!+2*2!+3*3!+...+n*n!
求数列an=(2n-1)(2n+1)(2n+3)前n项的和 求和:1*1!+2*2!+3*3!+...+n*n!

求数列an=(2n-1)(2n+1)(2n+3)前n项的和 求和:1*1!+2*2!+3*3!+...+n*n!
(1)Sn=1*3*5+3*5*7+5*7*9+……+(2n-1)(2n+1)(2n+3)
=1*3*5+1/8*(3*5*7*9-1*3*5*7)+1/8*(5*7*9*11-3*5*7*9)+……+1/8*[(2n-1)(2n+1)(2n+3)(2n+5)-(2n-3)(2n-1)(2n+1)(2n+3)]
=15/8+(2n-1)(2n+1)(2n+3)(2n+5)/8
(2)
1*1!+2*2!+3*3!+...+n*n!
=(2-1)*1!+(3-1)*2!+(4-1)*3!+...+(n+1-1)*n!
=(2!-1!)+(3!-2!)+(4!-3!)+……+【(n+1)!-n!】
=(n+1)!-1