已知数列{an}满足a1=1/4,a2=3/4,a(n+1)=2an-a(n-1)(n>等于2,n属于N*),数列{bn}满足：b1等于2,n属于N*),数列{bn}的前n项和为Sn(1)求证:数列{an}为等差数列(2)求证:数列{bn-an}为等比数列(3)若当且仅当n=4时,Sn取得

Question

已知数列{an}满足a1=1/4,a2=3/4,a(n+1)=2an-a(n-1)(n>等于2,n属于N*),数列{bn}满足：b1<0,3bn-b(n-1)=n(n>等于2,n属于N*),数列{bn}的前n项和为Sn
(1)求证:数列{an}为等差数列
(2)求证:数列{bn-an}为等比数列
(3)若当且仅当n=4时,Sn取得最小值,求b1的取值范围

Answer 1

1.a(n+1)-an=an-a(n-1)=...=a2-a1=1/2
2.an=n/2-1/4代入得bn-an=[b(n-1)-a(n-1)]/3
3.先把表达式求出来,算到第四项小于0,后面项大于0,自己算算就是了..