1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?

1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?
1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?

1/1*3+1/2*4+1/3*5+1/4*6+1/5*71+/6*8+1/7*9+1/8*10=?
=1/2*【（1-1/3）+（1/2-1/4）+（1/3-1/5）+.+（1/8-1/10）】
=1/2*（1+1/2-1/9-1/10）
=1/2*（3/2-19/90）
=1/2*（116/90）
=29/45

原式=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+1/(2*4)+1/(4*6)+1/(6*8)+1/(8*10)
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9)+(1/2)*(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10)
=(1/2)*(1-1/9+1/2-1/10)
=(1/2)*(58/45)
=29/45