已知数列{an}是首项a1=2的正项数列,且满足an^2=ana(n-1)+2[a(n-1)]^2(n>等于2且属
问题描述:
已知数列{an}是首项a1=2的正项数列,且满足an^2=ana(n-1)+2[a(n-1)]^2(n>等于2且属
且满足an^2=ana(n-1)+2[a(n-1)]^2(n>等于2且属于正整数)求数列{an}的通向公式
答
(an)^2=an*a(n-1)+2[a(n-1)]^2两边都减去[a(n-1)]^2得(an)^2-a(n-1)]^2=an*a(n-1)+[a(n-1)]^2[an+a(n-1)]*[an-a(n-1)]=a(n-1)[an+a(n-1)]∵[an+a(n-1)]>0∴an-a(n-1)=a(n-1)这下会了吧