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