lim(1/2+1/2^2...+1/2^n)/(1/3+1/3^2...1/3^n) 求极限
问题描述:
lim(1/2+1/2^2...+1/2^n)/(1/3+1/3^2...1/3^n) 求极限
lim(1/2+1/2^2...+1/2^n)/(1/3+1/3^2...1/3^n) 求极限
答
原式=lim(n->∞){[(1/2)(1-1/2^n)/(1-1/2)]/[(1/3)(1-1/3^n)/(1-1/3)]}
=[(1/2)/(1-1/2)]/[(1/3)/(1-1/3)]
=2.