数列{an}满足a1=1,a2=2,a(n+2)=(1+cos(nπ/2)^2)an+sin(nπ/2)^2,n=1,2,3,……
求a3,a4,并求数列{an}的通项公式.
人气:377 ℃ 时间:2019-08-18 22:13:49
解答
n为奇数时 sin(nπ/2)^2=1 偶数时为0
n为奇数时 1+cos(nπ/2)^2=0 偶数时为2
故n为奇数时 a n+2 = 0an +1 =1
n为偶数时 a n+2 = 2 an
故 an =
1 (n为奇数)
2^(n/2) (n为偶数)
故a3=1 a4=4
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