Question

12分之1加20分之1加30分之1一直加到90分之1等于多少?

12分之1加20分之1加30分之1加一直加到90分之1等于多少?

Answer 1

1/12+1/20+1/30+...+1/90 =(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+...+(1/9-1/10) =1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10 =1/3-1/10 =7/30

Answer 2

1/12+1/20+1/30+...1/90
=1/3x4+1/4x5+1/5x6 +...+1/9x10
=1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10
=1/3-1/10
=7/30

运用 1/n（n+1）=1/n-1/(n+1)