數學問題(20 marks)

✔ 最佳答案

X = (1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + ... + 1/2003 - 1/2004)= (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/2003 + 1/2004) -
2(1/2 + 1/4 + 1/6 + 1/8 + ... + 1/2002 + 1/2004)= (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... + 1/2003 + 1/2004) -
(1 + 1/2 + 1/3 + 1/4 + ... + 1/1001 + 1/1002)= 1/1003 + 1/1004 + 1/1005 + ... + 1/2003 + 1/2004
;
Y = (1/2006 + 1/2008 + 1/2010 + ... + 1/4006 + 1/4008)
;
X / Y
=
1/1003 + 1/1004 + 1/1005 + ... + 1/2003 + 1/2004
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1/2006 + 1/2008 + 1/2010 + ... + 1/4006 + 1/4008
=
2(1/2006 + 1/2008 + 1/2010 + ... + 1/4006 + 1/4008)
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1/2006 + 1/2008 + 1/2010 + ... + 1/4006 + 1/4008
= 2

回答 (1)