计算题【用简便方法】

1.
∵567+345×566=567+345×(567-1)
=567+567×345-345
=567×345+222
∴原式=1.
2.
∵ (71+1/6)×6/7=(70+7/6)×6/7=60+1=61
同理(61+1/5)×5/6=51,(51+1/4)×4/5=41,(41+1/3)×3/4=31
∴原式=61+51+41+31
=184.
4.原式=（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