Σ_{mathrm{k}=0}^{20}left({ }^{20} mathrm{C}_{mathrm{k}}right)^{2} is equal to :

English

Gujarati

Hindi

7.Binomial Theorem

hard

$\sum_{\mathrm{k}=0}^{20}\left({ }^{20} \mathrm{C}_{\mathrm{k}}\right)^{2}$ is equal to :

A

${ }^{40} \mathrm{C}_{21}$

B

${ }^{40} \mathrm{C}_{19}$

C

${ }^{40} \mathrm{C}_{20}$

D

${ }^{41} \mathrm{C}_{20}$

(JEE MAIN-2021)

Solution

$\sum_{\mathrm{k}=0}^{20}{ }^{20} \mathrm{C}_{\mathrm{k}} \cdot{ }^{20} \mathrm{C}_{20-\mathrm{k}}$

sum of suffix is const. so summation will be ${ }^{40} \mathrm{C}_{20}$

Standard 11

Mathematics

Share

Similar Questions

$\sum_{\substack{i, j=0 \\ i \neq j}}^{n}{ }^{n} C_{i}{ }^{n} C_{j}$ is equal to

normal

(JEE MAIN-2022)

Given $(1 – 2x + 5x^2 – 10x^3) (1 + x)^n = 1 + a_1x + a_2x^2 + ….$ and that $a_1^2\,= 2a_2$ then the value of $n$ is

normal

If $a$ and $d$ are two complex numbers, then the sum to $(n + 1)$ terms of the following series $a{C_0} – (a + d){C_1} + (a + 2d){C_2} – ……..$ is

hard

The value of $\left( \begin{array}{l}30\\0\end{array} \right)\,\left( \begin{array}{l}30\\10\end{array} \right) – \left( \begin{array}{l}30\\1\end{array} \right)\,\left( \begin{array}{l}30\\11\end{array} \right)$ + $\left( \begin{array}{l}30\\2\end{array} \right)\,\left( \begin{array}{l}30\\12\end{array} \right) + ……. + \left( \begin{array}{l}30\\20\end{array} \right)\,\left( \begin{array}{l}30\\30\end{array} \right)$

hard

(IIT-2005)

$\frac{{{C_1}}}{{{C_0}}} + 2\frac{{{C_2}}}{{{C_1}}} + 3\frac{{{C_3}}}{{{C_2}}} + …. + 15\frac{{{C_{15}}}}{{{C_{14}}}} = $

medium

(IIT-1962)