1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 要简便计算着急

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 要简便计算着急
1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 要简便计算
着急

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90 要简便计算着急
1/2＝1-1/2
1/6＝1/2-1/3
1/12＝1/3-1/4
…………………………
1/90＝1/9-1/10
则全加起来,等于1-1/10＝0.9

原式=1/2+1/2-1/3+1/3-1/4+...+1/9-1/10=1-1/10=9/10

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/9-1/10)
=1-1/10=9/10

(1-1/2)+(1/2-1/3)+(1/4-3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)=1-1/10=9/10
公式是:1-/n+1

1/2=1-1/2、1/6=1/2-1/3....1/90=1/9-1/10
原式=(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)+(1/9-1/10)=9/10=0.9