(1)
1-1/100^2=(99/100*101/100),1-1/2011^2=(2010/2011*2012/2011)
2)用你发现的规律计算:
(1-1/2^2)*(1-1/3^2)*......*(1-1/2010^2)*(1-1/2011^2)
=1/2*3/2*2/3*4/3*3/4*.*2010/2011*2012/2011
=1/2*2012/2011
=1006/2011
(1)
1-1/100^2=(99/100*101/100),1-1/2011^2=(2010/2011*2012/2011)
2)用你发现的规律计算:
(1-1/2^2)*(1-1/3^2)*......*(1-1/2010^2)*(1-1/2011^2)
=1/2*3/2*2/3*4/3*3/4*.*2010/2011*2012/2011
=1/2*2012/2011
=1006/2011