Binomial TheoremHard
Question
If (1 + x + 2x2)20 = a0 + a1x + a2x2 +......... + a40x40, then a0 + a2 + a4.......+ a38 is equal to :
Options
A.219 (230 + 1)
B.219(220 - 1)
C.220(219 - 1)
D.none of these
Solution
(1 + x + 2x2)20 = a0 + a1x +......... + a40x40
x = 1, then a0 + a1 +......... + a40 = 420
x = -1, then a0 - a1 + a2 -........ + a40 = 220
220 + 240 = 2[a0 + a2 +......... + a38 + a40]
a0 + a2 +......... + a38 = 219 + 239 - 220
= 219 (220 -1) ∵ a40 = a20
x = 1, then a0 + a1 +......... + a40 = 420
x = -1, then a0 - a1 + a2 -........ + a40 = 220
220 + 240 = 2[a0 + a2 +......... + a38 + a40]
a0 + a2 +......... + a38 = 219 + 239 - 220
= 219 (220 -1) ∵ a40 = a20
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