已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?

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已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?

已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?
已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?

已知数列{an}满足a1=2,a(n+1)-an=a(n+1)*an,则a31=?
a(n+1)-an=a(n+1)*an,
1/a(n+1)-1/an=-1
bn=1/an

b(n+1)-bn=-1,b1=1/2
等差数列,解出bn=1/2-(n-1)
得出an=1/bn,然后算a31.

a(n+1)=an/(1-an)
-0.033898305