(n→∞)lim(1-1/2²)(1-1/3²)...(1-1/n²)=?求详解

Question

(n→∞)lim(1-1/2²)(1-1/3²)...(1-1/n²)=?求详解

Answer 1

注意由平方差公式a²-b²=(a+b)(a-b)可以得到1-1/2²=(1 -1/2)(1+1/2)=1/2 *3/21-1/3²=(1 -1/3)(1+1/3)=2/3 *4/31-1/4²=(1 -1/4)(1+1/4)=3/4 *5/4……以此类推1-1/(n-1)²=(1 -1/n-1)(1+1...