1.
a(n+1)=3an
a(n+1)=3an=3*3a(n-1)=3^3*a(n-2)=……=3^(n-1)*a2=3^n*a1=3^(n+1)
an=3^n
2.
a(n+1)=an+1/(4n^2-1)
=an+1/[(2n+1)(2n-1)]
=an+(1/2)[(2n-1)-1/(2n+1)]
a(n+1)+1/(n+1/2)=an+1/(n-1/2)
a(n+1)+1/(n+1-1/2)=an+1/(n-1/2)=a(n-1)+1/(n-1-1/2)=……=a1+1/(1-1/2)=1/2-2=-3/2
an+1/(n-1/2)=-3/2
an=-1/(n-1/2)-3/2
3.
a(n+1)=2an+5
a(n+1)+5=2an+10=2(an+5)
an+5=(a1+5)2^(n-1)=6*2^(n-1)
an=6*2^(n-1)-5
4.
an=2n+1,数列{bn}中,b1=a1,当n大于等于2时,bn=abn-1（下标是bn-1）,则b4=,b5=（此题
b1=a1
b2=a[b(2-1)]=a(b1)=a(a1)=a(2+1)=a3=7
b3=a[b(3-1)]=a(b2)=a7=15
b4=a[b(4-1)]=a(b3)=a15=31
b5=a[b(5-1)]=a(b4)=a31=63
5.
an=2n/(3n+1)
=2/3-(2/3)/(3n+1)
=(2/3)[1-1/(3n+1)]
是递增数列.
6.
①a1=2,a(n+1)=an+(2n-1)
a(n+1)=an+(2n-1)
an=a(n-1)+(2n-3)
a(n-1)=a(n-2)+(2n-5)
……
a3=a2+(2*3-3)
a2=a1+(2*2-3)
叠加：
an-a1=2[n+(n-1)+……+3+2]-3(n-1)
=(n+2)(n-1)-3(n-1)
an=(n+2)(n-1)-3(n-1)+2