(1+1/1*3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/2007*2009)

(1+1/1*3)*(1+1/2*4)*(1+1/3*5)*.*(1+1/2007*2009)
=(2/3)*(2/3) *(3/2)*(3/4) *(4/3)*(4/5)*.*(2008/2007)*(2008/2009)
=(2/3)*(2008/2009)
=4016/6027(2/3)*(2/3) *(3/2)*(3/4) *(4/3)*(4/5)*.............*(2008/2007)*(2008/2009)这一步是怎么来的？抱歉，有点小错误，改一下(1+1/1*3)=(1*3-1)/(1*3)=[(2-1)(2+1)-1]/(1*3)=2²/(1*3)=(2/1)(2/3)(1+1/2*4)=(2*4-1)/(2*4)=[(3-1)(3+1)-1]/(2*4)=3²/(2*4)=(3/2)(4/3)其他类似 (1+1/1*3)*(1+1/2*4)*(1+1/3*5)*......*(1+1/2007*2009)=(2/1)*(2/3) *(3/2)*(3/4) *(4/3)*(4/5)*.............*(2008/2007)*(2008/2009)=(2/1)*(2008/2009)=4016/2009