2×4/1+4×6/1+6×8/1+.+2006×2008/1怎么计算?过程和结果都要!- 对不起 题目写错了.........应该是这样1/2×4+1/4×6+1/6×8+......+1/2006×2008
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![2×4/1+4×6/1+6×8/1+.+2006×2008/1怎么计算?过程和结果都要!- 对不起 题目写错了.........应该是这样1/2×4+1/4×6+1/6×8+......+1/2006×2008](/uploads/image/z/14564136-48-6.jpg?t=2%C3%974%2F1%2B4%C3%976%2F1%2B6%C3%978%2F1%2B.%2B2006%C3%972008%2F1%E6%80%8E%E4%B9%88%E8%AE%A1%E7%AE%97%3F%E8%BF%87%E7%A8%8B%E5%92%8C%E7%BB%93%E6%9E%9C%E9%83%BD%E8%A6%81%21-+%E5%AF%B9%E4%B8%8D%E8%B5%B7+%E9%A2%98%E7%9B%AE%E5%86%99%E9%94%99%E4%BA%86.........%E5%BA%94%E8%AF%A5%E6%98%AF%E8%BF%99%E6%A0%B71%2F2%C3%974%2B1%2F4%C3%976%2B1%2F6%C3%978%2B......%2B1%2F2006%C3%972008)
2×4/1+4×6/1+6×8/1+.+2006×2008/1怎么计算?过程和结果都要!- 对不起 题目写错了.........应该是这样1/2×4+1/4×6+1/6×8+......+1/2006×2008
2×4/1+4×6/1+6×8/1+.+2006×2008/1
怎么计算?过程和结果都要!
- 对不起 题目写错了.........应该是这样
1/2×4+1/4×6+1/6×8+......+1/2006×2008
2×4/1+4×6/1+6×8/1+.+2006×2008/1怎么计算?过程和结果都要!- 对不起 题目写错了.........应该是这样1/2×4+1/4×6+1/6×8+......+1/2006×2008
题目还是错了,应该改为:1/(2×4)+1/(4×6)+……+1/(2006×2008)
预备:假设0<a<b,那么
1/(a+b)=1/(b-a)·(1/a-1/b)
比如:1/(2×4)=1/(4-2)·(1/2-1/4)=1/2(1/2-1/4)
原式=1/2(1/2-1/4)+1/2(1/4-1/6)+1/2(1/6-1/8)+……+1/2(1/2006-1/2008)
=1/2(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2006-1/2008)
=1/2(1/2-1/2008)
=1/2(1003/2008)
=1003/4016
题目应该是:1/(2×4)+1/(4×6)+1/(6×8)+......+1/(2006×2008)
1/(2×4)+1/(4×6)+1/(6×8)+......+1/(2006×2008)
=1/4×[1/(1×2)+1/(2×3)+……+1/(1002×1003)+1/(1003×1004)]
=1/4×[1-1/2+1/2-1/3+1/3-1/4+……+1/1002-1/1003+1/1003+1/1004]
=1/4×[1-1/1004]
=1003/4016
2×4/1=2*4=8
4×6/1=4*6=24
6×8/1=6*8=48
题目好像有问题
怎么会有题目用除以1来表示?