已知{an},{bn}都是各项为正数的数列,都有an,bn^2,an+1成等差数列 ；bn^2,an+1,bn+1^2成等比数列,若a1=1,b1=根号2,求sn=1/a1+1/a2+…1/an
问题描述：
已知{an},{bn}都是各项为正数的数列,都有an,bn^2,an+1成等差数列 ；bn^2,an+1,bn+1^2成等比数列,若a1=1,b1=根号2,求sn=1/a1+1/a2+…1/an
答
∵bn²,a(n+1),b(n+1)²成等比数列 ∴bn² × b(n+1)²= a(n+1)²∵bn＞0,b(n+1)＞0,a(n+1)＞0∴bn × b(n+1) = a(n+1)……①∴b(n-1)×bn = an……②∵an,bn²,a(n+1)成等差数列.∴2bn...