Question

四则混合运算中的巧算(1-1/2*1/2)*(1-1/3*1/3)*.*(1-1/2005*1/2005)

Answer 1

答:1003/2005(1-1/2*1/2)*(1-1/3*1/3)*.*(1-1/2005*1/2005) =(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*(1-1/4)*(1+1/4)2003/2004*2005/2004*2004/2005*2006/2005=1/2*2006/2005=1003/2005