question_answer

Let \[S={{C}_{1}}-\left( 1+\frac{1}{2} \right)\,\,{{C}_{2}}+\left( 1+\frac{1}{2}+\frac{1}{3} \right)\,\,{{C}_{3}}-....+\] \[{{(-1)}^{n-1}}\left( 1+\frac{1}{2}....+\frac{1}{n} \right){{c}_{n}},\] then

A)  nS = 1                        

B)  1/S is an integer

C)  \[1/{{S}^{2}}\] is an integer    

D)  All of these

E)  None of these