已知数列an,a1=1,a2=3且a(n+2)=(1+2|cosnπ/2|)an+|sinnπ/2)|
（1）证明{a(2k)}为等比数列
人气：429 ℃ 时间：2020-06-05 12:35:13
解答
n=2k-1 (取奇数时）|cosnπ/2|= 0 ,|sinnπ/2|=11+2|cosnπ/2|=1上面的没用n=2k (取偶数时 )|cosnπ/2|= 1 ,|sinnπ/2|=01+2|cosnπ/2|=3a(n+2)=(1+2|cosnπ/2|)an+|sinnπ/2)|=3an+1a[(2k+1)]=3a[2(k)]+1a[(2k+1)]+...
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