已知数列{an},满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1(n≥2),则{an}的通项是

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已知数列{an},满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1(n≥2),则{an}的通项是已知数列{an},满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1(

已知数列{an},满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1(n≥2),则{an}的通项是
已知数列{an},满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1(n≥2),则{an}的通项是

已知数列{an},满足a1=1,an=a1+2a2+3a3+……+(n-1)an-1(n≥2),则{an}的通项是
an=a1+2*a2+…+(n-1)*an-1(n>=2)
an-1=a1+2*a2+…(n-2)*an-2(n>=3)
an-an-1=(n-1)*an-1(n>=3)
an=n*an-1
an=n*(n-1)*…*3*a2=n!*a2/2
a2=1=2!*a2/2
an=n!/2(n>=2)
an={1 n=1,
n!/2 n>=2.

an-n*an-1=(n-1)an-1
an=n*an-1
=...
=n*(n-1)*...*a2
又知道a2=1
an=n!/2
n的阶乘除以2