(1\2+1\6+1\12+1\20+1\30+1\42+1\56+1\72+1\90)除以1又1\9
1个回答

(12+16+112+120+130+142+156+172+190)÷ 1又19

= (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90) ÷ (1+1/9)

= {1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10) } ÷ (1+1/9)

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

= { 1-1/10 } ÷ (1+1/9)

= 9/10 ÷ 10/9

= 81/100