If ${\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ... + {C_n}{x^n}$, then the value of $\mathop \sum \limits_{0 \le r < s \le n} \sum \left( {r + s} \right)\left( {{C_r} + {C_s}} \right)$ is

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

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{\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ... + {C_n}{x^n}

, then the value of

\sum \limits_{0 \le r < s \le n} \sum \left( {r + s} \right)\left( {{C_r} + {C_s}} \right)

View answer and explanation

Correct option: A

{n^2}{.2^n}

Option A is correct because the value of the summation is found to be n² * 2^n by using properties of binomial coefficients and summations.

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