a=1/1X2+1/3X4+...........1/2003X2004 b=1/1003X2004+1/1004X2003+1/1005X2002+..........1/2004X1003 求a/b高中 回應 s87009812 Re: 難題 2006-07-16 16:32 非常妙的解答[From昌爸]: a=1/(1*2)+1/(3*4)+...+1/(2003*2004) =1-1/2+1/3-1/4+...+1/2003-1/2004 =1+1/2+1/3+...+1/2004-2(1/2+1/4+...+1/2004) =1+1/2+1/3+...+1/2004-(1+1/2+...+1/1002) =1/1003+1/1004+...+1/2004 b=1/(1003*2004)+1/(1004*2003)+...+1/(2003*1004)+1/(2004*1003) =2[1/(1003*2004)+1/(1004*2003)+...+1/(1503*1504)] =(2/3007)(1/1003+1/2004+1/1004+1/2003+...+1/1503+1/1504) =(2/3007)(1/1003+1/1004+...+1/2004) 所以 a/b=3007/2
s87009812 Re: 難題 2006-07-16 16:32 非常妙的解答[From昌爸]: a=1/(1*2)+1/(3*4)+...+1/(2003*2004) =1-1/2+1/3-1/4+...+1/2003-1/2004 =1+1/2+1/3+...+1/2004-2(1/2+1/4+...+1/2004) =1+1/2+1/3+...+1/2004-(1+1/2+...+1/1002) =1/1003+1/1004+...+1/2004 b=1/(1003*2004)+1/(1004*2003)+...+1/(2003*1004)+1/(2004*1003) =2[1/(1003*2004)+1/(1004*2003)+...+1/(1503*1504)] =(2/3007)(1/1003+1/2004+1/1004+1/2003+...+1/1503+1/1504) =(2/3007)(1/1003+1/1004+...+1/2004) 所以 a/b=3007/2
回應
s87009812
Re: 難題
2006-07-16 16:32a=1/(1*2)+1/(3*4)+...+1/(2003*2004)
=1-1/2+1/3-1/4+...+1/2003-1/2004
=1+1/2+1/3+...+1/2004-2(1/2+1/4+...+1/2004)
=1+1/2+1/3+...+1/2004-(1+1/2+...+1/1002)
=1/1003+1/1004+...+1/2004
b=1/(1003*2004)+1/(1004*2003)+...+1/(2003*1004)+1/(2004*1003)
=2[1/(1003*2004)+1/(1004*2003)+...+1/(1503*1504)]
=(2/3007)(1/1003+1/2004+1/1004+1/2003+...+1/1503+1/1504)
=(2/3007)(1/1003+1/1004+...+1/2004)
所以 a/b=3007/2