Question

2分之1加6分之1加12分之1加20分之1加30分之1加42分之1等于几

Answer 1

拆分法，2=1*2，6=2*3，12=3*4，以此类推，42=6*7，56=7*8，将式子拆分成1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8
可以看到。很多项可以抵消吧~~~最后等于7/8ps：*是乘号，/是除号~~~

Answer 2

1/2+1/6+1/12+1/20+1/30+1/42
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/7
=6/7

Answer 3

1/2+1/6+1/12+1/20+1/30+1/42=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)=1/2+1/2-1/7=6/7

Answer 4

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72
=(1-1/2)+(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)
=1-1/2+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
=1-1/9
=8/9

Answer 5

6/7