[1-(1/2)²][1-(1/3)²][1-(1/4)²]
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)
=(1/2)x(3/2)x(2/3)x(4/3)x(3/4)x(5/4)
=(1/2)x(5/4)
=5/8
其实靠的是平方差公式的应用,其实结果为(n+1)/(2n)
[1-(1/2)²][1-(1/3)²][1-(1/4)²]
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)
=(1/2)x(3/2)x(2/3)x(4/3)x(3/4)x(5/4)
=(1/2)x(5/4)
=5/8
其实靠的是平方差公式的应用,其实结果为(n+1)/(2n)