$\sum\limits_{k = 0}^{20} {{{\left( {{}^{20}{C_k}} \right)}^2}}$ is equal to :
Solution
$\sum\limits_{k = 0}^{20} {{{\left( {{}^{20}{C_k}} \right)}^2}}$
<br><br>= $${\left( {{}^{20}{C_0}} \right)^2} + {\left( {{}^{20}{C_1}} \right)^2} + {\left( {{}^{20}{C_2}} \right)^2} + .... + {\left( {{}^{20}{C_{20}}} \right)^2}$$
<br><br>= <sup>40</sup>C<sub>20</sub>
<br><br><b>Using the formula :</b>
<br><br>$${\left( {{}^n{C_0}} \right)^2} + {\left( {{}^n{C_1}} \right)^2} + {\left( {{}^n{C_2}} \right)^2} + .... + {\left( {{}^n{C_n}} \right)^2} = {}^{2n}{C_n}$$
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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