一道高二数列极限题已知：正项数列{An}和{Bn}中,A1=a (0

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一道高二数列极限题
已知：正项数列{An}和{Bn}中,A1=a (0

1.
Bn = (B(n-1))/(1-A(n-1)*A(n-1)) = (1 - A(n-1))/(1-A(n-1)*A(n-1))
=1/(1+A(n-1))
=>
An = A(n-1)/(1+An-1)
=>
An + An*An-1 = An-1
=>同除以AnAn-1
1/An = 1/An-1 + 1
=>
1/An = 1/A1 + n-1
=>
An = 1/(n-1+1/a)
2.
Cn = An*An/(1+An)
=1/(1/An + 1/An*An)
=1/(1/An + 1)*(1/An)
=1/(1/An) - 1/(1/An + 1)
=1/(1/An) - 1/(1/A(n+1))
=An - A(n+1)
=>
Sn = A1 - A(n+1)
n趋于正无穷时
Sn = A1 =a

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