${S_n} = \sum\limits_{r = 0}^n {\frac{1}{{^n{C_r}}}} $ एवं ${t_n} = \sum\limits_{r = 0}^n {\frac{r}{{^n{C_r}}}} $

${t_n} = \sum\limits_{r = 0}^n {\frac{{n – (n – r)}}{{^n{C_{n – r}}}}} $,

  = $n\sum\limits_{r = 0}^n {\frac{1}{{^n{C_r}}}}  – \sum\limits_{r = 0}^n {\frac{{n – r}}{{^n{C_{n – r}}}}} $

${t_n} = n\,.\,{S_n} – \left[ {\frac{n}{{^n{C_n}}} + \frac{{n – 1}}{{^n{C_{n – 1}}}} + ….. + \frac{1}{{^n{C_1}}} + 0} \right]$

${t_n} = n\,.\,{S_n} – \sum\limits_{r = 0}^n {\frac{r}{{^n{C_r}}}} $]

$ \Rightarrow $  ${t_n} = n\,.\,{S_n} – {t_n}$  $ \Rightarrow $ $2{t_n} = {\,^n}{S_n} \Rightarrow \frac{{{t_n}}}{{{S_n}}} = \frac{n}{2}$.