已知数列{an}的前n项和Sn满足Sn=2/3an-1/3,且1

问题描述:

已知数列{an}的前n项和Sn满足Sn=2/3an-1/3,且1

由题意得S1=2∕3a1-1/3=a1,∴a1=-1,∵Sk-Sk-1=(2/3ak-1/3)-(2/3ak-1-1/3)=2/3ak-2/3ak-1=ak,∴-1/3ak=2/3ak-1,即﹛an﹜是等比数列,且公比q=ak/ak-1=-2,∴ak=a1qˆk-1=-(-2)ˆk-1,又1〈Sk〈9,∴1<2/3[-(-2)&...