lim(n->∞)[(2/3)^(n+1)+1]/[(2/3)^n * 1/3+1/3]=3是怎么算出来的?书中例子:lim(n->∞) [2^(n+1) + 3^(n+1) ] / [2^n + 3^n] 分子分母同时除以3^(n+1)得到lim(n->∞)[(2/3)^(n+1)+1]/[(2/3)^n * 1/3+1/3],第二步书上结果直接等于3
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lim(n->∞)[(2/3)^(n+1)+1]/[(2/3)^n * 1/3+1/3]=3是怎么算出来的?
书中例子:lim(n->∞) [2^(n+1) + 3^(n+1) ] / [2^n + 3^n] 分子分母同时除以3^(n+1)得到lim(n->∞)[(2/3)^(n+1)+1]/[(2/3)^n * 1/3+1/3],第二步书上结果直接等于3,这个3是怎么算出来的?
分子分母都除以3^n
[2^(n+1)/3^n+3^(n+1)/3^n]/(2^n/3^n+3^n/3^n)
=[2*(2/3)^n+3]/[(2/3)^n+1]
lim(n->∞)(2/3)^n=0
lim(n->∞) [2^(n+1) + 3^(n+1) ] / [2^n + 3^n]
lim(n->∞)[2*(2/3)^n+3]/[(2/3)^n+1]=(2*0+3)/(0+1)=3
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