采用裂项消元的方法
原式=1/2*(1/3-1/5)+1/2*(1/5-1/7)+...+1/2*(1/1997-1/1999)
=1/2*(1/3-1/5+1/5-1/7...+1/1997-1/1999)
=1/2*(1/3-1/1999)
=998/5997
1/3*5+1/5*7+...+1/1997*1999
采用裂项消元的方法
原式=1/2*(1/3-1/5)+1/2*(1/5-1/7)+...+1/2*(1/1997-1/1999)
=1/2*(1/3-1/5+1/5-1/7...+1/1997-1/1999)
=1/2*(1/3-1/1999)
=998/5997