已知数列{an}满足a1=1,an+1=2an/an+2,写出数列的前五项,归纳一个通项公式
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已知数列{an}满足a1=1,an+1=2an/an+2,写出数列的前五项,归纳一个通项公式已知数列{an}满足a1=1,an+1=2an/an+2,写出数列的前五项,归纳一个通项公式已知数列{an}
已知数列{an}满足a1=1,an+1=2an/an+2,写出数列的前五项,归纳一个通项公式
已知数列{an}满足a1=1,an+1=2an/an+2,写出数列的前五项,归纳一个通项公式
已知数列{an}满足a1=1,an+1=2an/an+2,写出数列的前五项,归纳一个通项公式
a(n+1)=2an/(an+2)
1/a(n+1) = (an+2)/(2an)
= 1/2 + 1/an
1/a(n+1) -1/an = 1/2
1/an -1/a1 = (n-1)/2
1/an = (n+1)/2
an = 2/(n+1)
a2 = 2/3
a3 = 2/4 =1/2
a4 = 2/5
a5 =2/6 =1/3
1/an+1=(an+2)/(2an)=1/2+1/an
所以 1/an 是公差为1/2的等差数列
1/an=1/a1+(n-1)/2=(n+1)/2
an=2/(n+1)
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