已知数列{an}满足a1=4,an+1=2an/(an+2),
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已知数列{an}满足a1=4,an+1=2an/(an+2),
(1)求证:数列{1/an}是等差数列,(2)求an
抱歉,我打题目打错了 那个an+1应该等于2an/an+2(那个+2不是下标)
(1)求证:数列{1/an}是等差数列,(2)求an
抱歉,我打题目打错了 那个an+1应该等于2an/an+2(那个+2不是下标)
a(n+1)=2an/(an + 2)
取倒数得:
1/a(n+1)= (an + 2)/2an = 1/2 + 1/an
1/a(n+1) - 1/an = 1/2
所以{1/an} 为等差数列,公差是1/2 ,1/a1=1/4
1/an = 1/4 + 1*(n-1)/2 = (2n-1)/4
an = 4/(2n-1)
取倒数得:
1/a(n+1)= (an + 2)/2an = 1/2 + 1/an
1/a(n+1) - 1/an = 1/2
所以{1/an} 为等差数列,公差是1/2 ,1/a1=1/4
1/an = 1/4 + 1*(n-1)/2 = (2n-1)/4
an = 4/(2n-1)
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