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若lim[2n+(an^2+2n+1)/(bn+1)=1,则a+b

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3 | 2011-10-28 07:15:08 | 显示全部楼层 |阅读模式

lim(n->inf) [2n + (an2 + 2n + 1) / (bn + 1)] = 1lim (2bn2 + an2 + 4n + 1) / (bn + 1) = 1lim [(2b + a)n2 + 4n + 1] / (bn + 1) = 12b + a = 0，∵极限趋向常数，分子和分母的最高次方相同，都是n的一次方lim (4n + 1) / (bn + 1) = 1lim (4 + 1/n) / (b + 1/n) = 1(4 + 0) / (b + 0) = 1b = 4a = -2b = -8∴a + b = -8 + 4 = -4...

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