1+2+3+4+···+2005+2006)/(1-1/1004)*(1-1/1005)……(1-1/2005)*(1-1/2006)=
问题描述:
1+2+3+4+···+2005+2006)/(1-1/1004)*(1-1/1005)……(1-1/2005)*(1-1/2006)=
答
(1+2+3+4+···+2005+2006)/【(1-1/1004)*(1-1/1005)……(1-1/2005)*(1-1/2006)
分子=(1+2006)×2006÷2=2007×1003
分母=1003/1004×1004/1005×...×2004/2005×2005/2006
=1003/2006
=1/2
原式=2007×1003÷(1/2)
=2007×1003×2
=4026042