已知数列{an}满足a1=2,a(n+1)=(3an-2)/(2an-1),求证{1/(an-1)}是等差数列,并求数列{an}的通项公式
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已知数列{an}满足a1=2,a(n+1)=(3an-2)/(2an-1),求证{1/(an-1)}是等差数列,并求数列{an}的通项公式已知数列{an}满足a1=2,a(n+1)=(3an-2)/(
已知数列{an}满足a1=2,a(n+1)=(3an-2)/(2an-1),求证{1/(an-1)}是等差数列,并求数列{an}的通项公式
已知数列{an}满足a1=2,a(n+1)=(3an-2)/(2an-1),求证{1/(an-1)}是等差数列,并求数列{an}的通项公式
已知数列{an}满足a1=2,a(n+1)=(3an-2)/(2an-1),求证{1/(an-1)}是等差数列,并求数列{an}的通项公式
a(n+1)=(3an-2)/(2an-1)=(3an-3/2-1/2)/(2an-1)=3-1/[2(2an-1)]= →
a(n+1)=(3an-2)/(2an-1) → a(n+1)-1=(3an-2)/(2an-1)-1=(an-1)/(2an-1)
→ 1/[a(n+1)-1]=(2an-1)/(an-1)=1/(an-1)+2
∴1/(an-1)是公差为2的等差数列
1/(a1-1)=1/(2-1)=1,∴1/(an-1)=1+2(n-1)=2n-1
→ (an-1)=1/(2n-1)
→an=1+1/(2n-1)=2n/(2n-1)
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