Question

2/4*6+2/6*8+2/8*10+2/10*12+2/12*14

简便运算

Answer 1

解：2/4*6+2/6*8+2/8*10+2/10*12+2/12*14
=(1/4-1/6)+(1/6-1/8)+(1/8-1/10)+(1/10-1/12)+(1/12-1/14)
=1/4-1/14
=5/28

类似：1/[a*(a+n)]=(1/n)*[1/a-1/(a+n)]

例子：
1/56=1/(7*8)=1/7-1/8
1/12=1/(2*6)=(1/4)*[1/2-1/6]
....................
等等

这个式子是很有用的
以上希望对你有所帮助~

Answer 2

= 2/（2×2×2×3）+2/（2×2×3×4）+2/（2×2×4×5）+2/（2×2×5×6）+2/（2×2×6×7）
=1/[2×(2×3)]+1/[2×(3×4)]+1/[2×(4×5)]+1/[2×(5×6)]+1/[2×(6×7)]
=1/2×[1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)]
=1/2×[1/2－1/7]
=1/2×9/14
=9/28

Answer 3

2/4*6+2/6*8+2/8*10+2/10*12+2/12*14
=(1/4-1/6)+(1/6-1/8)+(1/8-1/10)+(1/10-1/12)+(1/12-1/14)
=1/4-1/14
=5/28