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求极限lim(1-1/2)(1-1/3)(1-1/4)...(1-1/n)=lim（x→∞）(l-1/4)(1-1/9)..(1-1/n^2)=
题目详情
求极限lim(1-1/2)(1-1/3)(1-1/4)...(1-1/n)=
lim（x→∞）(l-1/4)(1-1/9)..(1-1/n^2)=
lim（x→∞）(l-1/4)(1-1/9)..(1-1/n^2)=
▼优质解答
答案和解析
lim(1-1/2)(1-1/3)(1-1/4)...(1-1/n)=lim(1/2)(2/3)(3/4).[(n-2)/(n-1)][(n-1)/n]=lim1/n=0
lim(l-1/4)(1-1/9)..(1-1/n^2)
=lim(1-1/2)(1-1/3)(1-1/4)...(1-1/n)*(1+1/2)(1+1/3)(1+1/4)...(1+1/n)
=lim1/n *(n+1)/2
=1/2
lim(l-1/4)(1-1/9)..(1-1/n^2)
=lim(1-1/2)(1-1/3)(1-1/4)...(1-1/n)*(1+1/2)(1+1/3)(1+1/4)...(1+1/n)
=lim1/n *(n+1)/2
=1/2
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