1.
x,y是實數, x十y=3,2^x-2^y=1 ,2^x十2^y=k則k=?
2.
1/1十1/(1十2)十1/(1十2十3)十.....十1/(1十2十3十...十20)=?
2007-02-28 15:04:28 · 3 個解答 · 發問者 Y6745199907 2 in 教育與參考 ➔ 考試
1. 2x＋2y = k
k2 = (2x＋2y)2
= 22x＋2*2x2y＋22y
= 22x - 2*2x2y＋22y＋4*2x2y
= (2x - 2y)2 ＋4*2x＋y
= 12＋4*23
= 33
k = √33
2. 1/1＋1/(1＋2)＋1/(1＋2＋3)＋...＋1/(1＋2＋3＋...＋20)
= Σ120 1/[n(n＋1)/2]
= Σ120 2/[n(n＋1)]
= 2[(1/1 - 1/2)＋(1/2 - 1/3)＋(1/3 - 1/4)＋...＋(1/20 - 1/21)]
= 2[1 - 1/21]
= 40/21
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2007-03-01 07:49:00 · answer #1 · answered by JJ 7 · 0⤊ 0⤋
1. √33
2. 40/21
2007-02-28 15:35:39 · answer #2 · answered by tom 6 · 0⤊ 0⤋
1/1十1/(1十2)十1/(1十2十3)十.....十1/(1十2十3十...十20)=?
答案是121
2007-02-28 15:10:21 · answer #3 · answered by 負一 2 · 0⤊ 0⤋