1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?
1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 简便运算怎么算?
1/m(m+1)=1/m-1/(m+1)
原式=(1/1-1/2)+（1/2-1/3）+（1/3-1/4）+(1/4-1/5)+(1/5-1/6)+（1/6-1/7）
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7

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