Question

已知Sn是数列{an}的前n项和,且满足Sn=2An-(2的n+1次方) 证明数列{An/(2的n次方)}是等差数列

急求答案,谢谢大家快来答

Answer 1

Sn=2An-2^(n+1) (1)S(n-1)=2A(n-1)-2^n (2)(1)-(2) An=2An-2A(n-1)-2^nAn=2A(n-1)+2^nAn/2^n=A(n-1)/2^(n-1)+1令An/2^n=BnBn=B(n-1)+1∴{An/(2的n次方)}是公差为1的等差数列