2002乘20032003-2003乘20022002
=2002x20032003-(2002+1)20022002
=2002x20032003-2002x20022002-20022002
=2002(20032003-20022002)-20022002
=2002x10001-20022002
=2002x1001-2002x1001
=0
2+4+6+8+···+2004
=1005006
当n==1002时,
s=1002×(1002+1)=1005006.
即2+4+6+8+…+2004=1005006.
0.888乘125乘73+999乘3
125(0.8+0.08+0.008)x73+999x3
=(100+10+1)x73+111x9x3
=111x73+111x27
=111x100
=11100
1×3×5+3×5×7+5×7×9+…+101×103×105
=1*3*5+(3*5*7*9-1*3*5*7)/8+(5*7*9*11-3*5*7*9)/8+...+(101*103*105*107-99*101*103*105)/8
=1*3*5+(101*103*105*107-1*3*5*7)/8
=15+(116877705-105)/8
=15+14609700
=14609715
--------------------------------
原理:
n*(n+2)*(n+4)=[n(n+2)(n+4)(n+6)-(n-2)n(n+2)(n+4)]/8
