作业帮7/6 + 13/12 +21/20+31/30+43/42+57/56+73/72+91/90 简便计算
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7/6 + 13/12 +21/20+31/30+43/42+57/56+73/72+91/90 简便计算
7/6 + 13/12 +21/20+31/30+43/42+57/56+73/72+91/90 简便计算
7/6 + 13/12 +21/20+31/30+43/42+57/56+73/72+91/90 简便计算
将7/6等化为1又1/x,看x的规律,得8+[n/（2n+6）],数一下n是8,所以得8+（8/22）
7/6 + 13/12 +21/20+31/30+43/42+57/56+73/72+91/90
=1+1+1+1+1+1+1+1+(1/2-1/3+1/3-1/4+……+1/9-1/10)
=8+(1/2-1/10)
=8.4
你去问数学家吧？
＝8+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
＝8+1/4+1/12+1/24+1/40
＝8+1/3+1/15
＝8+2/5
＝8.4
应用的是两个整数分之一相加等于这两个整数的积分之这两个整数的和，因此两个一结合就简便了。
原式=（1+1/6）+(1+1/12)+(1+1/20)+(1+1/30)+(1+1/42)+(1+1/56)+(1+1/72)+(1+1/90)
=1×8+(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=8+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)...
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原式=（1+1/6）+(1+1/12)+(1+1/20)+(1+1/30)+(1+1/42)+(1+1/56)+(1+1/72)+(1+1/90)
=1×8+(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=8+1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)+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+1/2-1/3+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=17/2-1/10=42/5
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7/6 + 13/12 +21/20+31/30+43/42+57/56+73/72+91/90
=1+1+1+1+1+1+1+1+（1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=1+1+1+1+1+1+1+1+（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+0.4
=8.4