19+199+1999+19999+199999
=(20-1)+(200-1)+(2000-1)+(20000-1)+(200000-1)
=222220-5
=222215
2.1*3*24+2*6*48+3*9*72
------------------
1*2*4+2*4*8+3*6*12
=[1*3*24*(1+2*2*2+3*3*3)]/[1*2*4(1+2*2*2+3*3*3)]
=1*3*24/1*2*4
=9
3.1又2分之1+2又6分之1+3又12分之1+4又20分之1.+20又420分之1+21又462分之1
=(1+2+3+...+21)+(1/2+1/6+1/12+...+1/462)
=(1+21)*21/2+(1/1*2+1/2*3+1/3*4+...+1/21*22)
=231+(1-1/2+1/2-1/3+1/3-1/4+...+1/21-1/22)
=231+1-1/22
=230-1/22
=229又21/22
4.99+99*99+999*999*999
==99*(99+1)+999*(1000*999-1*999)
=99*100+999*(999000-999)
=9900+999*998001
=9900+(1000-1)*998001
=9900+1000*998001-998001
=9900+(998001000-998001)
=9900+997002999
=997012899