{an},{bn}中a1=2,b1=4,an,bn,an+1成等差数列bn,an+1,bn+1成等比数列(n∈N*)(2)证明:1/(a1+b1)+1/(a2+b2)+…1/(an+bn)<5/12

问题描述:

{an},{bn}中a1=2,b1=4,an,bn,an+1成等差数列bn,an+1,bn+1成等比数列(n∈N*)
(2)证明:1/(a1+b1)+1/(a2+b2)+…1/(an+bn)<5/12

(2)由已知得an=n(n+1),bn=(n+1)^2,所以an+bn=2n^2+3n+1>2n^2+2n=2n(n+1),所以1/an+bn