Question

若数列{an}是正项数列,且根号下a1+根号下a2+.+根号下an=n的平方+3n(n属于正整数）则a1/2+a2/3+

Answer 1

√a1+√a2+…+√a(n-1)+√an=n²+3n

√a1+√a2+…+√a(n-1) =(n-1)²+3(n-1)

两式相减得√an=2n+2

∴an=4(n+1)²

∴an/(n+1)=4(n+1)=4n+4

∴a1/2+a2/3+...+an/(n+1)

=4(1+2+...+n)+4n

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

=2n²+6n