数列{an}满足a1=1,a2=2,an+2=(1-1/3cos^2nπ/2)an+2sin^2nπ/2 求a3,a4及数列的通项公式 设Sn=a1+a2+...an求S2n

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数列{an}满足a1=1,a2=2,an+2=(1-1/3cos^2nπ/2)an+2sin^2nπ/2 求a3,a4及数列的通项公式 设Sn=a1+a2+...an
求S2n

(1)根据 a(1)=1、a(2)=2 及 a(n+2)=[1-(1/3)cos²(nπ/2)]a(n)+2sin²(nπ/2)可得 a(3)=[1-(1/3)cos²(π/2)]a(1)+2sin²(π/2)=[1-(1/3)×0]×1+2×1=3a(4)=[1-(1/3)cos²(2π/2)]a(2)+2sin&...