Write down the general term in the binomial expansion of \({{\left( \frac{{{x}^{2}}}{4}+\frac{2}{x}

Question

Write down the general term in the binomial expansion of ${{\left( \frac{{{x}^{2}}}{4}+\frac{2}{x} \right)}^{18}}.$ Write down the power of $x$ in this general term. Hence, or otherwise, determine the term independent of $x$ in the binomial expansion of ${{\left( \frac{{{x}^{2}}}{4}+\frac{2}{x} \right)}^{18}}.$

Accepted Answer

(i) $T_{r+1}=\binom{18}{r}\left(\frac{x^2}{4}\right)^{18-r}\left(\frac{2}{x}\right)^r$ (ii) $36-3r$ (iii) $18564$

Binomial Theorem - General Terms and Coefficients in Binomial Expansions

Binomial Theorem - General Terms and Coefficients in Binomial Expansions

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