Question

逆向运用等式1/a-1/b=b-a/ab,如1/12=4-3/3×4=1/3-1/4.根据上述等式计算：1+1/2+1/

Answer 1

1/k(k+1)=1/k-1/(k+1)

1+1/2+1/6+1/12+…+1/n(n+1)

=1+1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)=1+1-1/(n+1)=(2n+1)/(n+1)