${{\left( x-\frac{a}{{{x}^{2}}} \right)}^{n}}$ is expanded in descending powers of $x$, where \(

Question

${{\left( x-\frac{a}{{{x}^{2}}} \right)}^{n}}$ is expanded in descending powers of $x$, where $n$ is a positive integer and $a>0$. If the fifth term of the expansion is independent of $x$ and is equal to $7920$, find the value of $n$ and of $a$.

Accepted Answer

$n=12,\ a=2$

Binomial Theorem - Finding Parameters in Binomial Expansions

Binomial Theorem - Finding Parameters in Binomial Expansions

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