Question

1+三分之一+六分之一+十分之一+十五分之一+二十一分之一+二十八分之一+三十六分之一+四十五分之一是多少？

简便方式，要有步骤

Answer 1

1+三分之一+六分之一+十分之一+十五分之一+二十一分之一+二十八分之一+三十六分之一+四十五分之一

1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45
=1+1/3+1/2-1/3+1/10+1/15+1/21+1/28+1/36+1/45
=1+1/2+1/10+1/15+1/21+1/28+1/36+1/45
=1+1/2+1/3*(1/2-1/5)+1/2*(1/3-1/5)+1/4*(1/3-1/7)+1/3*(1/4-1/7)+1/5*(1/4-1/9)+1/4*(1/5-1/9)

=1+1/2+1/3*1/2-1/3*1/5+1/2*1/3-1/2*1/5+1/4*1/3-1/4*1/7+1/3*1/4-1/3*1/7+1/5*1/4-1/5*1/9+1/4*1/5-1/4*1/9

=1+1/2+1/3*1/2+1/2*1/3-1/3*1/5-1/2*1/5+1/4*1/3+1/3*1/4-1/4*1/7-1/3*1/7+1/5*1/4+1/4*1/5-1/5*1/9-1/4*1/9

=1+1/2+1/3-1/3*1/5-1/2*1/5+1/6-1/4*1/7-1/3*1/7+1/10-1/5*1/9-1/4*1/9

=1+1/2+1/3+1/6-1/3*1/5-1/2*1/5-1/4*1/7-1/3*1/7+1/10-1/5*1/9-1/4*1/9

=1+1-1/3*1/5-1/2*1/5-1/4*1/7-1/3*1/7+1/10-1/5*1/9-1/4*1/9

=2-1/3*1/5-1/2*1/5-1/4*1/7-1/3*1/7+1/10-1/5*1/9-1/4*1/9

=2-(1/3+1/2)*1/5-(1/4+1/3)*1/7+1/10-(1/5+1/4)*1/9

=2-5/6*1/5-7/12*1/7+1/10-(9/20)*1/9

=2-1/6-1/12+1/10-1/20

=2-1/6-1/12+1/10-1/20

=2-1/2+1/3-1/3+1/4-1/4+1/5+1/10

=2-1/2+1/5+1/10

=1+1-1/2+1/5+1/10

=1+1/2+1/5+1/10

=1+5/10+2/10+1/10

=1+8/10

=1+4/5

=9/5

Answer 2

• 两支粗细不同的蜡烛，长的能燃烧7小时短的能烧10小时，点燃4小时后两支蜡烛长度相等原来蜡烛长7m短蜡烛长