这道数列题怎么做
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题目是这样的http://hi.baidu.com/zc65671909/album/item/652588c9f15eec457d3e6f7f.html#
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易得 a[n]² = 1/(4n-3)
设b[n] = S[2n+1]-S[n]
研究b[n]的单调性
b[n+1] - b[n] = S[2n+3]-S[n+1] - S[2n+1] + S[n]
= a[2n+2]+a[2n+3]-a[n+1]
= 1/(8n+5) + 1/(8n+9) - 1/(4n+1)
< 1/(8n+2) + 1/(8n+2) - 1/(4n+1) < 0
∴ b[n]递减
∴ b[n] ≤ b[1] = a[2]²+a[3]³ = 1/5+1/9 = 14/45
t ≥ 28/3 , t∈N+
∴ t ≥ 10 即 t的最小值为10
设b[n] = S[2n+1]-S[n]
研究b[n]的单调性
b[n+1] - b[n] = S[2n+3]-S[n+1] - S[2n+1] + S[n]
= a[2n+2]+a[2n+3]-a[n+1]
= 1/(8n+5) + 1/(8n+9) - 1/(4n+1)
< 1/(8n+2) + 1/(8n+2) - 1/(4n+1) < 0
∴ b[n]递减
∴ b[n] ≤ b[1] = a[2]²+a[3]³ = 1/5+1/9 = 14/45
t ≥ 28/3 , t∈N+
∴ t ≥ 10 即 t的最小值为10
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