快,数列{An}的前n项和为Sn,a1=1,S（n+1）=4An+2,若Bn=A（n+1）-2An,

快,数列{An}的前n项和为Sn,a1=1,S（n+1）=4An+2,若Bn=A（n+1）-2An,

(1)∵数列{a[n]},S[n+1]=4a[n]+2∴S[n+2]=4a[n+1]+2将上面两式相减,得：a[n+2]=4a[n+1]-4a[n]即：a[n+2]-2a[n+1]=2(a[n+1]-2a[n])∵b[n]=a[n+1]-2a[n]∴b[n+1]=2b[n]∵S[n+1]=4a[n]+2∴a[2]+a[1]=4[1]+2∵a[1]=1∴a[2]=5∴b[1]=a[2]-2a[1]=3∴{b[n]}是首项为3,公比为2的等比数列即：b[n]=3*2^(n-1)(2)∵c[n]=1/(a[n+1]-2a[n])∴c[n]=1/b[n]=1/3*2^(n-1)∴c[1]=1/3,c[2]=1/6,c[3]=1/12,c[4]=1/24,c[5]=1/48,c[6]=1/96(3)∵由(1)知：a[n+1]-2a[n]=3*2^(n-1)两边除以2^(n+1),得：a[n+1]/2^(n+1)-2a[n]/2^(n+1)=3/4即：a[n+1]/2^(n+1)-a[n]/2^n=3/4∵d[n]=a[n]/2^n∴d[n+1]-d[n]=3/4∵a[1]=1∴d[1]=a[1]/2^1=1/2∴{d[n]}是首项为1/2,公差为3/4的等差数列即：d[n]=1/2+3/4(n-1)=(3n-1)/4

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