一道数学题（须巧妙解答）

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

1*2分之1 + 2*3分之1 + 3*4分之1 + 4*5分之1 + 5*6分之1+ 6*7分之1
=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

=1-1/2+1/2-1/3+1/3.....-1/6+1/6-1/7
=6/7
注意：1/a*（a+1）=1/a-1/(1+a)