Question

(1-1/2*1/2)*(1-1/3*1/3)*(1-1/4*1/4)...*(1-1/2005*1/2005)怎样简便

Answer 1

原式=[(2*2-1)/(2*2)]*[(3*3-1)/(3*3)]……[(2005*2005-1)/(2005*2005)]

=[(2-1)*(2+1)/(2*2)]*[(3-1)*(3+1)/(3*3)]……[(2005-1)*(2005+1)/(2005*2005)]

=[(1*3) /(2*2)]*[(2*4)/(3*3)]……[(2004*2006)/(2005*2005)]

=(1/2)*(2006/2005)

=1003/2005