Question

1/2=1/1乘2=1-1/2,1/6=1/2乘3=1/2-1/3,1/12=1/3乘4=1/3-1/4......观察这组等式的规律，完成下列各题：

（1）1/1乘2+1/2乘3+......+1/10乘11=
（2）若1/1乘3+1/3乘5+......+1/11乘13+n/13=-1

若二题都对者，追加50分！

Answer 1

(1)原式=1-1/2+1/2-1/3+1/3-1/4+。。。+1/10-1/11=10/11
（2）原式=1/2（1-1/3+1/3-1/5+。。。+1/11-1/13）+n/13=6/13+n/13=-1
所以n=-19

Answer 2

（1）1/1乘2+1/2乘3+......+1/10乘11
=(1-1/2)+(1/2-1/3)+……+(1/10-1/11)
=1-1/2+1/2-1/3+……+1/10-1/11
=1-1/11
=10/11

（2）若1/1乘3+1/3乘5+......+1/11乘13+n/13=-1
1/2(1-1/3)+1/2(1/3-1/5)+……+1/2(1/11-1/13)+n/13
=1/2(1-1/3+1/3-1/5+……+1/11-1/13)+n/13
=1/2(1-1/13)+n/13
=1/2x12/13+n/13
=6/13+n/13
=(6+n)/13
=-1
6+n=-13
n=-19

Answer 3

（1）原式=1-1/11=10/11
(2)n=-19

追问

我不要答案，过程and思路，懂？

追答

1）1/1乘2+1/2乘3+......+1/10乘11
=(1-1/2)+(1/2-1/3)+……+(1/10-1/11)
=1-1/2+1/2-1/3+……+1/10-1/11
=1-1/11
=10/11

（2）
原式=1/2（1-1/3+1/3-1/5+。。。+1/11-1/13）+n/13=6/13+n/13=-1
得n/13=-19/13，n=-19