已知数列{an}满足A1=0,A(N+1)=AN减去根号三/根号三AN加1.求A2,A3,A4,A5,A6N为正整数_数学解答

已知数列{an}满足A1=0,A(N+1)=AN减去根号三/根号三AN加1.求A2,A3,A4,A5,A6
N为正整数

人气：187 ℃　时间：2020-04-09 22:33:09

解答

A(n+1)=An-√3/(√3+1)
=An-√3(√3-1)/2
=An-3/2+√3/2
A2=3/2-√3/2
A3=A2-(-3/2+√3/2)=3-√3
A4=A3-(-3/2+√3/2)=9/2-3√3/2
A5=6-2√3
A6=15/2-5√3/2