Obtain the first three terms in the expansion of ${{\left( 1\mathrm{ }+x+{{x}^{2}} \right)}^{6}}$

Question

Obtain the first three terms in the expansion of ${{\left( 1\mathrm{ }+x+{{x}^{2}} \right)}^{6}}$ in ascending powers of $x$. Hence, find the term independent of $x$ in the expansion of ${{\left( 1-\frac{1}{3x} \right)}^{2}}{{(1+x+{{x}^{2}})}^{6}}.$

Accepted Answer

(i) $1+6x+21x^2+\cdots$ (ii) $-\frac{2}{3}$

Binomial Theorem - Binomial Expansion for Positive Integer Powers

Binomial Theorem - Binomial Expansion for Positive Integer Powers

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