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（1-1/2）*（1+1/2）*（1-1/3）*（1+1/3）*（1-1/4）*（1+1/4）*.*（1+1/2004）*（1-1/2004）
（1-1/2）*（1+1/2）*（1-1/3）*（1+1/3）*（1-1/4）*（1+1/4）*.*（1+1/2004）*（1-1/2004）
=（1/2)*(3/2)*(2/3)*(4/3)*.(2003/2004)*(2005/2004)
=(1/2)*(2005/2004)
=2005/4008
(1/2+1/3+1/4+.+1/2004)(1+1/2+.+1/2004)-(1+1/2+.+1/2005)(1/2+1/3+.+1/2004)=?
calculation
Let 1 / 2 + 1 / 3 + 1 / 4 +. + 1 / 2004 = n, then
simple form
= n(1+n)-(1+n+1/2005)n
= n(1+n-1-n-1/2005)
= -n/2005
(the title seems to be wrong, please confirm it again)
What is the value of 1 / 5 + 2 / 5 ^ 2 + 3 / 5 ^ 3 +. + 2004 / 5 ^ 2004?
Let s = 1 / 5 + 2 / 5 ^ 2 + 3 / 5 ^ 3 +. + 2004 / 5 ^ 2004, then 5S = 1 + 2 / 5 + 3 / 5 ^ 2 +. + 2004 / 5 ^ 2003 subtraction: 4S = 1 + 1 / 5 + 1 / 5 ^ 2 +. + 1 / 5 ^ 2003-2004 / 5 ^ 2004, the first 2004 terms form an equal ratio sequence, and calculate by yourself
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