已知数列｛an｝中,满足an-(2/an)=2n,且an

Question

已知数列｛an｝中,满足an-(2/an)=2n,且an

Answer 1

(1)
an-(2/an)=2n
(an)^2-2n·an-2＝0
an=n±√(n^2+2)
由于an{√[(n-1)^2]+√(n^2)-2n+1}/{√[(n-1)^2+2]+√(n^2+2)}=0
所以an>a(n-1)
{an}递增.