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在[{{}}的序列中,a1 = 1,a2 = 3,并且a + 2 = 3 an + 1是已知的。

 点击:次  发布日期:2019-05-25 19:51    发布人:365bet亚洲平台

质量响应
测试:(I)用+ 2 = 3 an + 1?2 a得到:a + 2?An + 1 = 2(a + 1?An),aa = 1,a2 = 3,即a 2 ?.如果a1 = 2,{an + 1-an}是2的第一阶,则比率是2,系列的比率是......(3分)a + 1-an = 2×2 n-1 = 2 n。..(4分)an = a1 +(a2-a1)+(a3-a2)+ ... +(an-an-1)= 1 + 2 + 22 + ... + 2 n-1 = 1?
2N1?
2 = 2n?...(7分)(II)bn = log 2(an + 1)= log 22 n = n,...(8分)Sn = n(n + 1)2,......(9分)1 Sn = 2 n(N + 1)= 2(1 n?)
1n + 1),1S1 + 1S2 + 1S3 + ... + 1Sn = 2[(1?
12)+(12?
13)+ ... +(1 n?)
1n + 1)]= 2(1?
1n + 1)<2 ...(14分)