question_answer

If\[{{S}_{n}}=\sum\limits_{r=0}^{n}{\frac{1}{^{n}{{C}_{r}}}}\]and\[{{t}_{n}}=\sum\limits_{r=0}^{n}{\frac{r}{^{n}{{C}_{r}}}}\]then\[\frac{{{t}_{n}}}{{{S}_{n}}}\]is equal to

A) \[\frac{n}{2}\]                  

B)                        \[\frac{n}{2}-1\]              

C)        \[n-1\]

D)        \[\frac{2n-1}{2}\]

Correct Answer: A

Solution :

Given that,