Question

对任意一个非零数,对他进行如下计算:

求它的倒数与1的差的倒数。现在请对下列各数-1，-2，-3，......，-10，-1/2，-1/3，-1/4，.....，-1/10分别进行这样的运算，再求所有结果的和~
过程

Answer 1

-1的倒数与1的差的倒数为-1/2
-2.....................................-2/3
-3.....................................-3/4
-4.....................................-4/5
-5.....................................-5/6
-6.....................................-6/7
-7.....................................-7/8
-8.....................................-8/9
-9.....................................-9/10
-10...................................-10/11
-1/2..................................-1/3
-1/3..................................-1/4
-1/4...................................-1/5
-1/5....................................-1/6
-1/6....................................-1/7
-1/7....................................-1/8
-1/8....................................-1/9
-1/9....................................-1/10
-1/10..................................-1/11
-1/2-2/3-3/4-4/5-5/6-6/7-7/8-8/9-9/10-10/11-1/3-1/4-1/5-1/6-1/7-1/8-1/9-1/10-1/11
=-9-1/2
负九又二分之一
好像太复杂了，不知谁有简便的方法

Answer 2

-1的倒数与1的差的倒数为-1/2
-2.....................................-2/3
-3.....................................-3/4
-4.....................................-4/5
-5.....................................-5/6
-6.....................................-6/7
-7.....................................-7/8
-8.....................................-8/9
-9.....................................-9/10
-10...................................-10/11
-1/2..................................-1/3
-1/3..................................-1/4
-1/4...................................-1/5
-1/5....................................-1/6
-1/6....................................-1/7
-1/7....................................-1/8
-1/8....................................-1/9
-1/9....................................-1/10
-1/10..................................-1/11
嗯，然后有-10的和-1/10的结果相加等于负一，你会发现塔门之间的规律，-9和-1/9也等于负一，，，，-8和-1/8等于负一，-7和-1/7。。。。。。。最后留下一个1/2，答案是9又1/2