数列{an}中,a1=1,an+1-2an=(n+2)/n/(n+1),则a2,a3,a4,分别为多少,猜想an=

数列{an}中,a1=1,an+1-2an=(n+2)/n/(n+1),则a2,a3,a4,分别为多少,猜想an=
数列{an}中,a1=1,an+1-2an=(n+2)/n/(n+1),则a2,a3,a4,分别为多少,猜想an=

数列{an}中,a1=1,an+1-2an=(n+2)/n/(n+1),则a2,a3,a4,分别为多少,猜想an=
an+1-2an=(n+2)/(n(n+1))
an+1=2an+(n+2)/n*(n+1)=2an+(n+2)/n-(n+2)/(n+1)=2an+2/n-1/(n+1)
an+1+1/(n+1)=2*(an+1/n)
所以：
{an+1/n}为等比数列,公比为2,首项为a1+1/1=1+1=2
an+1/n=2*2^(n-1)=2^n
an=2^n-1/n
当n=1,a1=1也满足an
所以an=2^n-1/n