教一道简算题

原式＝0.5[(1/2-1/4)+(1/3-1/5)+(1/4-1/6)……+(1/9-1/11)]
＝0.5(1/2+1/3-1/9-1/11)
＝125/198

1/2*4+1/3*5+1/4*6+1/5*7+…+1/8*10+1/9*11

=(1/2*4+1/4*6+...+1/8*10)+(1/3*5+1/5*7+...+1/9*11)

=1/2(1/2-1/4)+1/2(1/4-1/6)+...+1/2(1/8-1/10)+1/2(1/3-1/5)+...+1/2(1/9-1/11)

=1/2[1/2-1/4+1/4-1/6+...+1/8-1/10]+1/2[1/3-1/5+1/5-1/7+...+1/9-1/11]
=1/2[1/2-1/10]+1/2[1/3-1/11]
=2/10+4/33
=53/165

=(1/2)*(1/2-1/4+1/3-1/4+1/4-1/6+...+1/9-1/11)
=(1/2)*(1/2+1/3-1/10-1/11)
=53/165

1/2*4+1/3*5+1/4*6+1/5*7+…+1/8*10+1/9*11
=(1/2*4+1/4*6+1/6*8+1/8*10)+(1/3*5+1/5*7+1/7*9+1/9*11)
=(1/2)(2/2*4+2/4*6+2/6*8+2/8*10)+(1/2)*(2/3*5+2/5*7+2/7*9+2/9*11)
=(1/2)[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+(1/8-1/10)]+(1/2)[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=(1/2)(1/2-1/10)+(1/2)(1/3-1/11)
=1/5+4/33
=53/165

=4/2+5/3+2/3+7/5+4/3+9/7+5/4+11/9
=541/50

原式=1/2*(1/9-1/11)+1/2*(1/8-1/10)+1/2*(1/7-1/9)+1/2*(1/6