已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an

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已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an
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已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an
已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an

已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an
an=a1+(1/2)a2+(1/3)a3+...+[1/(n-2)]a(n-2)+[1/(n-1)]a(n-1)
a(n-1)=a1+(1/2)a2+(1/3)a3+...+[1/(n-2)]a(n-2)
an=a(n-1)+[1/(n-1)]a(n-1)=a(n-1)[n/(n-1)]
an/n=a(n-1)/(n-1)
a1/1=1/1=1
数列{an/n}是各项都为1的常数数列
an/n=1
an=n
n=1时,a1=1,同样满足.
数列{an}的通项公式为an=n.

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