(1-1/2^2)(1-1/3^2)……(1-1/2004^2)=？

来源：百度知道编辑：UC知道时间：2024/04/28 23:14:47

(1-1/2^2)(1-1/3^2)……(1-1/2004^2)=

1-1/n^2=(n^2-1)/n^2=(n-1)(n+1)/n^2

(1-1/2^2)(1-1/3^2)……(1-1/2004^2)
=1*3/2^2*2*4/3^2*3*5/4^2*...*2003*2005/2004^2
=(1*2005)/(2*2004)
=2005/4008.

0
1-1=0
0/任何数＝0
0乘任何数=0
所以最后还是0

2005/4008
不懂上HI百度

=(1+1/2)(1-1/2)(1+1/3)(1-1/3)...(1+1/2004)(1-1/2004)
=(1+1/2)(1+1/3)...(1+1/2004)((1-1/2)(1-1/3)...(1-1/2004)
=3/2*4/3*5/4*...*2005/2004*1/2*2/3*3/4*...*2003/2004
=2005/2 *1/2004
=2005/4008

原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)........(1-1/2004)(1+1/2004)
=(1-1/2)(1-1/3)......(1-1/2004)(1+1/2)(1+1/3).....(1+1/2004)
=(1/2)(2/3)(3/4)...(2003/2004)(3/2)(4/3）...(2004/2003)(2005/2004)
=(1/2)(2005/2004)
=2005/4008

1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1+1/1+2+1/1+2+3.........+1/1+2+3.....100 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=? (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) (1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2) 1/2-1/2=? 3/2=2+1/1*2=1/1+1/2 (1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)