哥哥教我简便计算

1*1/4+1/4*1/7+1/7*1/10+。。。。。。。+1/25*1/28
=[1/3]*[(4-1)/1*4+(7-4)/4*7+(10-7)/7*10+..........+(28-25)/25*28]
=(1/3)*[1-1/4+1/4-1/7+1/7-1/10+............+1/25-1/28]
=(1/3)*(1-1/28)
=9/28

1+1/1+2+1/1+2+3+1/1+2+3+4+......+1/1+2+3+4+5+6+7+8+9+10
=1+1/[(1+2)2/2]+1/[(1+3)3/2]+.......+1/[(1+10)10/2]
=2{1/2+1/2*3+1/3*4+.......1/10*11}
=2(1/2+1/2-1/3+1/3-1/4+......+1/10-1/11)
=2(1-1/11)
=20/11

1/2*7+7*12+1/12*17+......................1/2007*2012+1/2012*2017
=(1/5)[(7-2)/2*7+(12-7)/7*12+............+(2017-2012)/2012*2017]
=(1/5)*(1/2-1/2017)
=403/4034

1*1/4+1/4*1/7+1/7*1/10+。。。。。。。+1/25*1/28
=1/3*(1-1/4+1/4-1/7+1/7-1/10+--------+1/25-1/28)
=1/3(1-1/28)
=9/28

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+......+1/(1+2+3+4+5+6+7+8+9+10)
=2(1/2+1/6+1/12+----+1/110)
=2(1-1/2+1/2-1/3+1/3-1/4+----+1/10-1/11)
=2(1-1/11)=20/11

1/2*7+1/7*12+1/12*17+......................1/2007