女乡长下乡玩男村长:(1-1/2-1/3-1/4…-1/2005)*(1/2+1/3+1/4+…1/2006)-(1-1/2-1/3-1/4-…-1/2006)*(1/2+1/3+1/4+…+1/2005)
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设A=1-1/2-1/3-1/4…-1/2005
B=1/2+1/3+1/4+…+1/2005
则原式=A*(B+1/2006)-(A-1/2006)*B
=A*B+A*1/2006-A*B+B*1/2006
=(A+B)*1/2006
=1*1/2006
=1/2006
换元法
可以设1-1/2-1/3...1/2005为a
1+1/2+1/3...1/2005为b然后带入
答案应该是1/1003
1/2006
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
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+......+10
1/1+1/2+1/3+1/4+。。。。+1/N 是多少
(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*……*(1-1/99)*(1+1/99)。
(1+1/2)*(1-1/2)(1+1/3)*(1-1/3)*.......(1+1/99))*(1-1/99)怎么做
(1-1/2^2)(1-1/3^2)....(1-1/10^2)
(1-1/2^2)(1-1/3^2)....(1-1/10^2)
s=1/1+1/1!+1/2!+1/3!+1/4!+....+1/25!
3/2=2+1/1*2=1/1+1/2