数列an满足a1=1,a2=2,an+2=(cos^2×nπ/2)an+sin^2×nπ/2,则2013=() A.20
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数列an满足a1=1,a2=2,an+2=(cos^2×nπ/2)an+sin^2×nπ/2,则2013=() A.2013 B.3019 C.2 D.1
是否求S2013
∵a1=1,a2=2
a(n+2)=cos²(nπ/2)an+sin²(nπ/2)
∴a3=cos²(π/2)a1+sin²(π/2)=1
a5=cos²(5π/2)a3+sin²(5π/2)=1
.
a(2k-1)=1
a4=cos²(π)a2+sin²(π)=2
a6=cos²(2π)a4+sin²(2π)=2
.
a2k=2
∴S2013
=(a1+a3+.+a2013)+(a2+a4+.+a2012)
=1007+1006*2=3019
选C
再问: 应该是求a2013=
再答: a2013=1
∵a1=1,a2=2
a(n+2)=cos²(nπ/2)an+sin²(nπ/2)
∴a3=cos²(π/2)a1+sin²(π/2)=1
a5=cos²(5π/2)a3+sin²(5π/2)=1
.
a(2k-1)=1
a4=cos²(π)a2+sin²(π)=2
a6=cos²(2π)a4+sin²(2π)=2
.
a2k=2
∴S2013
=(a1+a3+.+a2013)+(a2+a4+.+a2012)
=1007+1006*2=3019
选C
再问: 应该是求a2013=
再答: a2013=1
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