In the expansion of ${{\left( \sqrt[3]{{{x}^{2}}}+3{{x}^{2}} \right)}^{n}}$, the sum of coefficien

Question

In the expansion of ${{\left( \sqrt[3]{{{x}^{2}}}+3{{x}^{2}} \right)}^{n}}$, the sum of coefficients of each term is $992$ more than the sum of the binomial coefficients, $\left( \begin{matrix} n \ r \ \end{matrix} \right)$, where $r=0,\,\,1,\,\,2,\,\,\ldots ,\,\,n$. Find the value of $n$ Hence find the term with the greatest coefficient in the expansion of ${{\left( \sqrt[3]{{{x}^{2}}}+3{{x}^{2}} \right)}^{n}}$.

Accepted Answer

(i) $n=5$ (ii) $405x^{26/3}$

Binomial Theorem - Sums of Coefficients in Polynomial Expansions

Binomial Theorem - Sums of Coefficients in Polynomial Expansions

Video Solution:

Solution:

Solution locked