Question

设数列{an}满足a1=2,an+1=an+1/an,(n∈N).令bn=an/根号下n,判断bn与bn+1的大小

Answer 1

a1=2,an+1=an+1/an,(n∈N).

bn=an/√n,

∴b-bn=(an+1/an)/√(n+1)-an/√n2k+1/2,那么

a^2=(ak+1/ak)^2>ak^2+2>2k+1/2+2=2(k+1)+1/2,

即n=k+1时①也成立,

∴对任意n∈N+,①成立

∴