Question

1/2+1/6+1/12+1/20+……+1/90+1/110+1/132

Answer 1

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