Find the constant term in the binomial expansion of \({{\left( x-\frac{1}{2{{x}^{3}}} \right)}^{8}}.

Question

Find the constant term in the binomial expansion of ${{\left( x-\frac{1}{2{{x}^{3}}} \right)}^{8}}.$ Given that the coefficient of $\frac{1}{{{x}^{4}}}$ in the expansion of ${{\left( 1+\frac{4}{{{x}^{2}}} \right)}^{n}}+{{\left( x-\frac{1}{2{{x}^{3}}} \right)}^{8}}$is $1049.$ Find $n$, where $n>0$.

Accepted Answer

(i) $7$ (ii) $n=12$

Binomial Theorem - General Terms and Coefficients in Binomial Expansions

Binomial Theorem - General Terms and Coefficients in Binomial Expansions

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