Question

数列{an}的前n项和Sn=a^n+b(a≠0且a≠1),证明数列{an}为等比数列的充要条件是b=-1

Answer 1

==>如果b=-1,a1=s1=a-1

an=sn-s(n-1)=a^n-a^(n-1)=(a-1)*a^(n-1) 当n>1

显然此时an是等比数列

1

所以等比q=a,所以a1=s1=a+b=a2/q=(a-1)*a/a=a-1 ==>b=-1