已知{an}满足a1=1,a(n+1)an+2(an+1)=an(n∈N*)(1)求数列{an}的通项公式;(2)求证a2/a1 + a3/a2 + …+a(n+1)/an <n/2
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已知{an}满足a1=1,a(n+1)an+2(an+1)=an(n∈N*)(1)求数列{an}的通项公式;(2)求证a2/a1 + a3/a2 + …+a(n+1)/an <n/2
已知{an}满足a1=1,a(n+1)an+2(an+1)=an(n∈N*)
(1)求数列{an}的通项公式;
(2)求证a2/a1 + a3/a2 + …+a(n+1)/an <n/2
已知{an}满足a1=1,a(n+1)an+2(an+1)=an(n∈N*)(1)求数列{an}的通项公式;(2)求证a2/a1 + a3/a2 + …+a(n+1)/an <n/2
a(n+1)an+2(an+1)=an 1+2/(an)=1/(a(n+1)) 令1/an=bn b(n+1)-2bn=1 b(n+1)+1=2(bn+1) 令bn+1=cn c(n+1)=2cn c2=2c1 c3=2c2.cn=2c(n-1)(n>1) cn=2^(n-1)c1因为a1=1
c1=2 cn=2^n an=1/(2^n-1)
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