Question

1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4

Answer 1

1...1/n(n+1)=1/n-1/(n+1)

证明:1/n-1/(n+1)=[(n+1)-n]/[n(n+1)]=1/n(n+1)

2...1/（x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)

=1/(x-3)-1/(x-2)-2/(x-1)(x-3)+1/(x-2)-1/(x-1)

=1/(x-3)-2/(x-1)(x-3)-1/(x-1)

=0