雖然全身酸痛, 但我還是晾在床上把朋友"那麼藍" 他兒子遇到的數學難題運算了一下, 他在BBS上請教大家如何用小學六年級學生能理解的方式來解這道題。結果! 結果!!! 偶居然算不出來...555....看來小學六年級要回去重讀了, 真丟人。
誰算的出來, 偶給他一個超大的愛的鼓勵。
題目:
2004的2倍減去2004的1/2，再加2004的3倍減去2004的2/3，再加2004的4倍減去2004的3/4……一直加到2004的2004倍減去2004的2003/2004。
我到後來卡住的運算:
2004×2－2004×1/2＋2004×3－2004×2/3＋2004×4－2004×3/4＋……＋2004×2004－2004×2003/2004
=2004[(2+3+4+……+2004)－(1/2+2/3+3/4+……＋2003/2004)]
=2004{[(1001×2006)－(1/2+2/3+3/4+……＋2003/2004)]}
=2004{2008006－[(1－1/2)＋(1－1/3)＋(1－1/4)＋……＋(1－1/2004)]}
=2004{2008006－[2003－(1/2＋1/3＋1/4＋……＋1/2004)]}
=4,024,044,024－4,014,012＋2004(1/2＋1/3＋1/4＋……＋1/2004)
=4,020,030,012＋2004(1/2＋1/3＋1/4＋……＋1/2004)
I may be wrong but I don't think this is a primary-school-level arithmetic problem. Anyway, here is my comment.
The series
1/1, 1/2, 1/3, 1/4, 1/5,..., 1/n
has been shown to diverge.
The sum of the series is approximately ln(n)+0.5772156649.
To continue your calculation, I add the following lines.
=4020030012+2004x[1/1+1/2+1/3+......+1/2004-1]
~4020030012+2004x[ln(2004)+0.5772156649-1]
~4020030012+2004x[7.6029004622+0.5772156649-1]
=4020030012+2004x7.1801161271
~4020044401
Wow! It's not easy being a parent these days.
Dear,
But the problem is, the kid is just an elementary school student, we can not use ln(n), calculus or any computer. I even didn't use calculator when I operated.
Thanks for your answer anyway. Not only to be good parents, but we also have fun when we enjoy the mathematics which had faded from our memory. Agree? :)
By the way, 我覺得有可能是運用消去法來簡化算式, 但我沒找到它的規律 :(
Posted by: Jocelyn at January 4, 2005 12:01 PM这个。。。。
似乎要用到我高中时候学的一个求和公式哈。。。。。
小学6年级做这样的题。。。汗
估计
我们很多人都要回去重读了
55555
這個好玩
2+3+4+.....+2004=0+1+2+3+4+....+2004-1
=2004*2004/2+1002(中間點)-1
=2009009此部份應為如此才對
整個程式2004{[(2004×1002+1002-1)－(1/2+2/3+3/4+……＋2003/2004)]}
=2004{[(2004×1002)－(1+1/2+2/3+3/4+……＋2003/2004)+1002]}
接下的問題就是如何用加減乘除來算
(1+1/2+2/3+3/4+……＋2003/2004)了
一定要算出答案嗎?
我只把規則先寫出來而已...
2004*{(1又1/2)+(2又1/3)+(3又1/4)+...+(2003又1/2004)}
Posted by: 佩文 at January 13, 2005 11:31 PMAs for the Giants, their own happiness was short-lived as they lost to - who else?
Posted by: asefarrel at June 18, 2006 09:14 AM