怎么答这两道题
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怎么答这两道题怎么答这两道题怎么答这两道题1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2004×2005)=1-1/2+1/2-1/3+1/3-1/4+...+1/2004-1/20
怎么答这两道题
怎么答这两道题
怎么答这两道题
1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2004×2005)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2004-1/2005
=1-1/2005
=2004/2005
1/(1×3)+1/(3×5)+1/(5×7)+...+1/(49×51)
=1/2×(1-1/3+1/3-1/5+1/5-1/7+...+1/49-1/51)
=1/2×(1-1/51)
=1/2×50/51
=25/51