+2*2!+3*3!+4*4!……n*n!
问题描述：
+2*2!+3*3!+4*4!……n*n!
答
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答
设x=1!+2*2!+3*3!+4*4!……n*n!两边同时加上1!+2!+3!+4!……n!
得 x+(1!+2!+3!+4!……n!)
=2*1!+3*2!+4*3!+……(n+1)n!=2!+3!+……(n+1)!
所以x+(1!+2!+3!+4!……n!)=2!+3!+……(n+1)!
x=(n+1)!-1