数列an满足a1=1,a2=2,an+2=(1-1/3cos^2n*π/2)+2sin^2*π/2,（1）求a3、a4及数列an的通项公式（2）设S...数列an满足a1=1,a2=2,an+2=(1-1/3cos^2n*π/2)+2sin^2*π/2,（1）求a3、a4及数列an的通项公式（2）设Sn＝a1＋a2＋…＋an,求Sn.
问题描述：
数列an满足a1=1,a2=2,an+2=(1-1/3cos^2n*π/2)+2sin^2*π/2,（1）求a3、a4及数列an的通项公式（2）设S...
数列an满足a1=1,a2=2,an+2=(1-1/3cos^2n*π/2)+2sin^2*π/2,（1）求a3、a4及数列an的通项公式（2）设Sn＝a1＋a2＋…＋an,求Sn.
答
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答
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答
n为奇数时 cos^2n*π/2=0 sin^2*π/2=1 an+2=1+2=3
n为偶数时 cos^2n*π/2=1 sin^2*π/2=0 an+2=1-1/3+0=2/3
an=1 n=1
an=2 n=2
an=3 n>2且n为奇数时
an=2/3 n>2且n为偶数时