JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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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: C

\frac{1}{2} n

Option C (

\frac{{1}}{{2}} n

) is correct because by using the property

{}^n C_r = {}^n C_{n-r}

and summing the series, we can find that

t_n = \frac{n}{2} s_n

, thus

\frac{t_n}{s_n} = \frac{n}{2}

More Questions from BINOMIAL THEOREM

Practice All Chapter MCQs →

\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n