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

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

问答/217℃/2024-10-21 22:09:30

优质解答：

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

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