已知数列{an}满足:a1=2a,an=2a-a*a/an-1(n(-N*,n>=2).bn=1/an-a1.求证BN是等差数列.2.求数列AN的通项公式.
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已知数列{an}满足:a1=2a,an=2a-a*a/an-1(n(-N*,n>=2).bn=1/an-a1.求证BN是等差数列.2.求数列AN的通项公式.
已知数列{an}满足:a1=2a,an=2a-a*a/an-1(n(-N*,n>=2).bn=1/an-a
1.求证BN是等差数列.
2.求数列AN的通项公式.
已知数列{an}满足:a1=2a,an=2a-a*a/an-1(n(-N*,n>=2).bn=1/an-a1.求证BN是等差数列.2.求数列AN的通项公式.
(1)\
b1=1/(a1-a)=1/a
bn-bn-1=1/(an-a)-1/(an-1-a) (把an=2a-a*a/an-1带入并化简)
=1/a (n》2)
所以 bn是等差数列
(2)、
bn = n/a
bn=1/an-a
所以 an=(n+1)n/a
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