The coefficient of t^4 in the expansion of&nb | vedclass

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Question

$\left(1-t^{6}\right)^{3}(1-t)^{-3}$

$\left(1-t^{18}-3 t^{6}+3 t^{12}\right)(1-t)^{-3}$

$\Rightarrow$ coefficient of $t^{4}$ in $(1-t)^{-3}$ is

Vedclass · Accepted Answer

$15$

Vedclass · Answer

$\left(1-t^{6}\right)^{3}(1-t)^{-3}$

$\left(1-t^{18}-3 t^{6}+3 t^{12}\right)(1-t)^{-3}$

$\Rightarrow$ coefficient of $t^{4}$ in $(1-t)^{-3}$ is

$^{3+1-1} C_{4}=^{6} C_{2}=15$

The coefficient of $t^4$ in the expansion of ${\left( {\frac{{1 - {t^6}}}{{1 - t}}} \right)^3}$ is

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