1-1/2+1/3-1/4+.......-1/40= N/M 求證N為61的倍數國中 發表回應前，請先登入 回應 訪客 (未驗證) Re: 難題----求救！ 2004-06-10 21:07 1-1/2+1/3-1/4........-1/40=N/M =1+1/2+1/3+1/4......+1/40-2*(1/2+1/4+1/6.....+1/40) =1+1/2+1/3+.....+1/40 - (1+1/2+1/3+1/6...+1/20) =1/21+1/22+1/23.......+1/40 =(1/21+1/40)+(1/22+1/39)+.......(1/30+1/31) =61/(21*40) + 61/(22*39) + ..... +61/(30*31) =61 * ( 1/(21*40)+1/(22*39)+...+1/(30*31) ) =61 * P/Ｍ ＝ Ｎ／Ｍ 所以Ｎ為６１的倍數
訪客 (未驗證) Re: 難題----求救！ 2004-06-10 21:07 1-1/2+1/3-1/4........-1/40=N/M =1+1/2+1/3+1/4......+1/40-2*(1/2+1/4+1/6.....+1/40) =1+1/2+1/3+.....+1/40 - (1+1/2+1/3+1/6...+1/20) =1/21+1/22+1/23.......+1/40 =(1/21+1/40)+(1/22+1/39)+.......(1/30+1/31) =61/(21*40) + 61/(22*39) + ..... +61/(30*31) =61 * ( 1/(21*40)+1/(22*39)+...+1/(30*31) ) =61 * P/Ｍ ＝ Ｎ／Ｍ 所以Ｎ為６１的倍數
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訪客 (未驗證)
Re: 難題----求救！
2004-06-10 21:07=1+1/2+1/3+1/4......+1/40-2*(1/2+1/4+1/6.....+1/40)
=1+1/2+1/3+.....+1/40 - (1+1/2+1/3+1/6...+1/20)
=1/21+1/22+1/23.......+1/40
=(1/21+1/40)+(1/22+1/39)+.......(1/30+1/31)
=61/(21*40) + 61/(22*39) + ..... +61/(30*31)
=61 * ( 1/(21*40)+1/(22*39)+...+1/(30*31) )
=61 * P/Ｍ ＝ Ｎ／Ｍ
所以Ｎ為６１的倍數