Question

乘积(1-1/2的平方)(1-1/3的平方).(1-1/2005的平方) 的值是多少?

Answer 1

=[1^2-(1/2)^2][1^2-(1/3)^2]...[1^2-(1/2005)^2]

=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2005)(1-1/2005)

=3/2*1/2*4/3*2/3*...*2006/2005*2004/2005

=(3/2*4/3*5/4*...*2006/2005)*(1/2*2/3*3/4*...*2004/2005)

=1003*1/2005

=1003/2005

逆用平方差公式