Question

在数列｛an｝中,a1=2,an+1=4an-3n+1,n属于正整数 (1)证明｛an-n｝是等比数列 (2)求数列｛a

Answer 1

an+1=4an-3n+1

an+1-(n+1)=4[an-n]

[an+1-(n+1)]/[an-n]=4等比a1-1=3

an-n=3*4^(n-1)

an=3*4^(n-1)+n

2 sn=[3*4^(n-1)-3]/3+n(1+n)/2=

3 Sn+1=4^n -1+[n+1][n+2]/2

4sn=4^n-4+2n(1+n)-Sn+1≥0