Math miscellaneousHard
Question
Coefficient of x79 in the expansion of (x + x2 + x4)20 is equal to -
Options
A.0
B.150x319
C.1
D.320
Solution
Let (x + x2 + x4)20 = a0 + a1x + .... + a79x79 + a80x80
Replace x by
⇒ (1 + x2 + x3)20 = a80 + a79x + ....... + a0x80
Diff. w.r.t. x
(2x + 3x2).20(1 + x2 + x3)19 = a79 + 2a78x + .....
Put x = 0
a79 = 0
Replace x by
⇒ (1 + x2 + x3)20 = a80 + a79x + ....... + a0x80
Diff. w.r.t. x
(2x + 3x2).20(1 + x2 + x3)19 = a79 + 2a78x + .....
Put x = 0
a79 = 0
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