Question

1/10*11+1/11*12+1/12*13+......+1/19*20如何简便计算

Answer 1

由于1/10*11=1/10-1/11
1/11*12=1/11-1/12
1/12*13=1/12-1/13
..................
..................
所以原式==(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+......+(1/19-1/20)
=1/10-1/11+1/11-1/12+1/12-1/13+......+1/19-1/20
=1/10-1/20
=1/20

Answer 2

1/10*11+1/11*12+1/12*13+......+1/19*20
=(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+......+(1/19-1/20)
=1/10-1/11+1/11-1/12+1/12-1/13+......+1/19-1/20
=1/10-1/20
=1/20

Answer 3

原式=(1/10-1/11)+(1/11-1/12)+......+(1/19-1/20)
（每一项的第2个和后一项的第1个消掉）
=1/10-1/20=1/20

这叫裂项相消法

Answer 4

1/10*11+1/11*12+1/12*13+......+1/19*20
=1/10-1/11+1/11-1/12+1/12-1/13+1/13......-1/19+1/19-1/20
=1/10-1/20
=1/20