作业帮找规律进行简便计算7/6 + 13/12 + 21/21 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90怎样简便啊?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/12 12:21:49
找规律进行简便计算7/6 + 13/12 + 21/21 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90怎样简便啊?
找规律进行简便计算
7/6 + 13/12 + 21/21 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90
怎样简便啊?
找规律进行简便计算7/6 + 13/12 + 21/21 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90怎样简便啊?
7/6 + 13/12 + 21/21 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90
=[(2*3+1)/2*3]+[(3*4+1)/3*4]+[(4*5+1)/4*5]+[(5*6+1)/5*6]+[(6*7+1)/6*7]+...
=1+1/2*3+1+1/3*4...
=8+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+...
=8+1/2-1/3+1/3-1/4+1/4-1/5...
=8+1/2-1/10
=8.4
原式=6/6+1/6+12/12+1/12+20/20+1/20+30/30+1/30+42/42+1/42+56/56+1/56+72/72+1/72+90/90+1/90
=1+1/2-1/3+1+1/3-1/4+1+1/4-1/5+1+1/5-1/6+1+1/6-1/7+1+1/7-1/8+1+1/8-1/9+1+1/9-1/10
=8+1/2-1/10
=8+4/10
=8+0.4
=8.4
7/6 + 13/12 + 21/20 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90
=8+(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=8+(1/2-1/3+1/3-1/4+---------+1/9-1/10)
=8+(1/2-1/10)
=8+0.4
=8.4
首先每一项提出 1 之后 就是 1+1/6+1+1/12+1+1/20+1+1/30+1+1/42+1+1/56....
之后 合并1 1/6看成是1/2-1/3 1/12看成是 1/3-1/4 以此类推
得到的是 8+1/2-1/10=8.4
第三项应该是21/20吧？如果是则:先每项提1出来=1+1/6+1+1/12+1+1/20……+1+1/90=8+(1/2*3+1/3*4+……1/9*10)=8+(1/2-1/3)+(1/3-1/4)…(1/9-1/10)=8又2/5
7/6 + 13/12 + 21/20 + 31/30 + 43/42 + 57/56 + 73/72 + 91/90
=1+1/(2×3)+1+1/(3×4)+1+1/(4×5)+1+1/(5×6)+1+1/(6×7)+1+1/(7×8)+1+1/(8×9)+1+1/(9×10)
=8+(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)=8+1/2-1/10=8.4