1/2+1/6+1/12+1/20+……+1/90+1/110+1/132跪 你们谁的对

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132跪 你们谁的对
1/2+1/6+1/12+1/20+……+1/90+1/110+1/132
跪
你们谁的对

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132跪 你们谁的对
我们给出的答案实际上都是一样的,就看你觉得哪个过程比较容易懂,不过其实都没差别
1/2+1/6+1/12+1/20+……+1/90+1/110+1/132
=1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+…+1/(9x10）+1/(10x11)+1/(11x12)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+（1/4-1/5)+…+(1/9-1/10)+(1/10-1/11)+(1/11-1/12)
=1-1/12
=11/12

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10+1/10-/11+1/11-1/12
=1-1/12
=11/12

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132
＝1-½+½-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10+1/10-1/11+1/11-1/12
＝1+（-½+½)+(-1/3+1/3)+(-1/4+1/4)+……+(-1/9+1/9)+(-1/10+1/10)+(-1/11+1/11)-1/1...

全部展开

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132
＝1-½+½-1/3+1/3-1/4+1/4-1/5+……+1/9-1/10+1/10-1/11+1/11-1/12
＝1+（-½+½)+(-1/3+1/3)+(-1/4+1/4)+……+(-1/9+1/9)+(-1/10+1/10)+(-1/11+1/11)-1/12
=1+0+0+0+……+0+0+0-1/12
＝1-1/12
＝11/12

收起

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10+1/10-/11+1/11-1/12
=1-1/12
=11/12应该没错