Question

数列{an}是正项数列,√a1+√a2+……+√an=n^2+3n,则a1/2=a2/3+……a/(n+1)的和为多少

Answer 1

应该是求A1/2+A2/3+……+An/(n+1)的和吧

√A1+√A2+……+√An=n^2+3n

n>=2时,

√A1+√A2+……+√A(n-1)=(n-1)^2+3(n-1)

两式相减

√An=n^2+3n-(n-1)^2-3(n-1)=2n+2

An=4(n+1)^2

√A1=1+3=4 A1=16也满足上式

An/(n+1)=4(n+1)

A1/2+A2/3+……+An/(n+1)

=4(2+n+1)n/2=2n(n+3)