Question

Binomial Q..

Answer 1

\[S _{n} = \sum_{r=0}^{n}\frac{1 }{ \left(\begin{matrix}n \\ r\end{matrix}\right) }\] and \[Tn = \sum_{r=0}^{n}\frac{ r }{ \left(\begin{matrix}n \\ r\end{matrix}\right) }\] then tn/sn =?

Answer 2

@ganeshie8

Answer 3

.

Answer 4

@freckles

Answer 5

@imqwerty

Answer 6

@samigupta8 can you help?

Answer 7

Hi.

You can write\[T_n =\sum_{r=0}^{n}\frac{r}{\binom{n}r}=\sum_{r=0}^n \frac{n-r}{\binom{n}{n-r}} = \sum_{r=0}^{n}\frac{n-r}{\binom{n}r}\]So\[T_n + T_n = \sum_{r=0}^n \frac{r}{\binom{n}r} + \sum_{r=0}^n \frac{n-r}{\binom{n}r} = \sum_{r=0}^n \frac{n}{\binom{n}r}=nS_n\]\[\Rightarrow 2T_n = nS_n\]\[\Rightarrow T_n/S_n = n/2\]

Answer 8

wonderful!!

Answer 9

Thanks!

Answer 10

No problem. :'(