The coefficient of t4 in the expansion of [( 1 - t^6 1 - t )^3] is :

Question

The coefficient of t4 in the expansion of $${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$ is :

Accepted Answer

$${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$

=  (1 - t6)3 (1 - t)-3

=  (1 - 3C1t6 + 3C2t12 - 3C3t18) $$ \times $$ (1 - t)-3

coefficient of t4 is 1 $$ \times $$ coefficient of t4 in (1 - t)-3

=  1 $$ \times $$ 3+4-1C4  (By multinomial theorem)

= 6C4 = 15

Solutions · 1