If ${S_n} = \mathop \sum \limits_{r = 0}^n \frac{1}{{{\;^n}{C_r}}}$ and ${t_n} = \mathop \sum \limits_{r = 0}^n \frac{r}{{{\;^n}{C_r}}}$ then $\frac{{{t_n}}}{{{s_n}}}$ is equal to

JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

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Analyzing +4 | -1

{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

View answer and explanation

Correct option: A

\frac{n}{2}

Option A (

\frac{n}{2}

) is correct because it is derived by manipulating the summation formulas and using properties of binomial coefficients.

Practice All Chapter MCQs →

m \times n

m

n

A

B

{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

n