已知数列{an}满足a1=1,a2=2/3,且a(n-1)an+ana(n+1)-2a(n-1)a(n+1)=0(n≥2),求a3,a4.
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已知数列{an}满足a1=1,a2=2/3,且a(n-1)an+ana(n+1)-2a(n-1)a(n+1)=0(n≥2),求a3,a4.已知数列{an}满足a1=1,a2=2/3,且a(n-1)an
已知数列{an}满足a1=1,a2=2/3,且a(n-1)an+ana(n+1)-2a(n-1)a(n+1)=0(n≥2),求a3,a4.
已知数列{an}满足a1=1,a2=2/3,且a(n-1)an+ana(n+1)-2a(n-1)a(n+1)=0(n≥2),求a3,a4.
已知数列{an}满足a1=1,a2=2/3,且a(n-1)an+ana(n+1)-2a(n-1)a(n+1)=0(n≥2),求a3,a4.
等式两边同除以a(n-1)ana(n+1)
1/a(n+1) +1/a(n-1)-2/an=0
2/an =1/a(n+1) +1/a(n-1)
1/a2 -1/a1=1/(2/3) -1/1=1/2
数列{1/an}是以1为首项,1/2为公差的等差数列.
1/an=1 +(1/2)(n-1)=(n+1)/2
an=2/(n+1)
数列{an}的通项公式为an=2/(n+1)
a3=2/(3+1)=1/2
a4=2/(4+1)=2/5
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