第十题怎么做啊，跪求详细解答过程
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比较 (2^n+1)/(3^n-1) 与 (2^n)/(3^n) 的极限情况
lim [(2^n+1)/(3^n-1)] / [(2^n)/(3^n)]
= lim [(2^n+1)/(2^n)] / [(3^n)/(3^n-1)]
因为：lim (2^n+1)/(2^n) = lim (1+1/2^n) = 1
lim (3^n)/(3^n-1) = lim 1/(1-1/3^n) = 1
所以 lim [(2^n+1)/(2^n)] / [(3^n)/(3^n-1)] = 1
这说明 (2^n+1)/(3^n-1) 与 (2^n)/(3^n) 的极限相同
又因为 lim (2^n)/(3^n) = 0
所以 lim = (2^n+1)/(3^n-1) = 0
lim [(2^n+1)/(3^n-1)] / [(2^n)/(3^n)]
= lim [(2^n+1)/(2^n)] / [(3^n)/(3^n-1)]
因为：lim (2^n+1)/(2^n) = lim (1+1/2^n) = 1
lim (3^n)/(3^n-1) = lim 1/(1-1/3^n) = 1
所以 lim [(2^n+1)/(2^n)] / [(3^n)/(3^n-1)] = 1
这说明 (2^n+1)/(3^n-1) 与 (2^n)/(3^n) 的极限相同
又因为 lim (2^n)/(3^n) = 0
所以 lim = (2^n+1)/(3^n-1) = 0
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