a(n+1)=2an+n+1
a(n+1)+(n+1)+2=2an+2n+4=2(an +n+2)
[a(n+1)+(n+1)+2]/(an +n+2)=2,为定值
a1+1+2=1+1+2=4,数列{an+n+2}是以4为首项,2为公比的等比数列
an +n+2=4×2^(n-1)=2^(n+1)
an=2^(n+1)-n-2
n=1时,a1=2²-1-2=1,同样满足通项公式
数列{an}的通项公式为an=2^(n+1) -n-2
a(n+1)=2an+n+1
a(n+1)+(n+1)+2=2an+2n+4=2(an +n+2)
[a(n+1)+(n+1)+2]/(an +n+2)=2,为定值
a1+1+2=1+1+2=4,数列{an+n+2}是以4为首项,2为公比的等比数列
an +n+2=4×2^(n-1)=2^(n+1)
an=2^(n+1)-n-2
n=1时,a1=2²-1-2=1,同样满足通项公式
数列{an}的通项公式为an=2^(n+1) -n-2