1/(5×6×7)+1/(6×7×8)+1/(7×8×9)+…+
来源:百度知道 编辑:UC知道 时间:2024/06/20 05:17:13
计算1/(5×6×7)+1/(6×7×8)+1/(7×8×9)+…+1/(80×81×82)
要有解题过程
要有解题过程
首先,我们知道:1/(5×6)=1/5-1/6;1/(6×7)=1/6-1/7;……以此类推
接下来:1/(5×6×7)=1/2×[1/(5×6)-1/(6×7)]=1/2×[1/5-1/6-(1/6-1/7)]
=1/2×(1/5-1/7)
那么:1/(6×7×8)=1/2×(1/6-1/8)
…………以此类推
之后把中间项都可以消去,但要注意,最开始的1/5和1/6两项,以及最后的1/81和1/82两项,这四项是不能消掉的~~
所以最后该式可化为:=1/2×(1/5+1/6-1/81-1/82)=5681/16605
……得出这个结果我也感觉很意外……
1/(k*(k-1)*(k+1)) = 1/2(k-1) + 1/2(k+1)-1/k
=> 1/2(1/5-2/6+1/7 + 1/6-2/7+1/8 + 1/7-2/8+1/9 + ... +1/80-2/81+1/82)
= 1/2(1/5-1/6 -1/81+1/82)
1/140
1/[5*82]
(3*4*5*6*7*8)(1/3+1/4+1/5+1/6+1/7+1/8)
(1/2-1)*(1/3-1)*(1/4-1)*(1/5-1)*(1/6-1)*(1/7-1)*(1/8-1)*(1/9-1)*(1/10-1)
1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+......+1/100 = ?
1/2+1/3+1/4+1/5+1/6+1/7+.......+1/99+1/100=?
1/2+1/3+1/4+1/5+1/6+1/7+……+1/2000+1/2001
数学问题:1/5+1/6+1/7+1/8+......+1/n=?
1/3+1/4+1/5+1/6+1/7的整数部分是几?
1/3+1/4+1/5+1/6+1/7 用哪个公式解?
1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+1/5*6*7
5x-1/6=7/3