1/6+1/12+1/20+1/30+1/42+1/56怎么简便计算?19/99+19/99×2+19/99×3+······+19/99×10
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 10:25:09
![1/6+1/12+1/20+1/30+1/42+1/56怎么简便计算?19/99+19/99×2+19/99×3+······+19/99×10](/uploads/image/z/34748-44-8.jpg?t=1%2F6%2B1%2F12%2B1%2F20%2B1%2F30%2B1%2F42%2B1%2F56%E6%80%8E%E4%B9%88%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%3F19%2F99%2B19%2F99%C3%972%2B19%2F99%C3%973%2B%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%2B19%2F99%C3%9710)
1/6+1/12+1/20+1/30+1/42+1/56怎么简便计算?19/99+19/99×2+19/99×3+······+19/99×10
1/6+1/12+1/20+1/30+1/42+1/56怎么简便计算?19/99+19/99×2+19/99×3+······+19/99×10
1/6+1/12+1/20+1/30+1/42+1/56怎么简便计算?19/99+19/99×2+19/99×3+······+19/99×10
第一题的关键在于看出分母的规律,然后求出分母的最小公倍数.1/6+1/12+1/20+1/30+1/42+1/56
=1/(2×3) + 1/(3×4) + 1/(4×5) + 1/(5×6) + 1/(6×7) + 1/(7×8)
=(4×5×7+2×5×7+2×3×7+4×7+4×5+3×5) / (2×3×4×5×7)
=315 / (2×3×4×5×7)
=(3×3×5×7)/ (2×3×4×5×7)
=3/8
第二题:先求出1、2、3、4、5、6、7、8、9、10的最小公倍数为:5×7×8×9.
19/99+19/99×2+19/99×3+······+19/99×10
=19×(1/99+1/99×2+1/99×3+······+1/99×10)
=19×(5×7×8×9+4×5×7×9+3×5×7×8+2×5×7×9+······+4×7×9)/99×5×7×8
然后算出结果
化简公式:[1/n(n+d)]=1/d*[(1/n)-1/(n+d)];
化简得:(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/7-1/8)=1/2-1/8=3/8;