Math miscellaneousEasy
Question
The coefficient of x13 in the expansion of (1 - x)5 (1 + x + x2 + x3)4 is :-
Options
A.4
B.-4
C.0
D.5
Solution
(1 - x)5 (1 + x)4 (1 + x2)4
⇒ (1 - x2)4 (1 + x2)4 (1 - x) = (1 - x4)4 (1 - x)
∴ Coefficient of x13 in
{(1 - x) (1 - 4x4 + 6x8 - 4x12 ...)} = 4
⇒ (1 - x2)4 (1 + x2)4 (1 - x) = (1 - x4)4 (1 - x)
∴ Coefficient of x13 in
{(1 - x) (1 - 4x4 + 6x8 - 4x12 ...)} = 4
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