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
Create a free account to view solution
View Solution FreeMore Binomial Theorem Questions
Middle term in the expansion of (x2 − 2x)10 will be -...In the expansion of (1 + 3x + 2x2)6 the coefficient of x11 is -...The number of non zero terms in the expansion of [(1 + 3√2x )9 − (1 − 3√2x)9] is -...The sum of coefficients of odd powers of x in the expansion of (1 + x)n is -...The coefficient of x5 in the expansion of (2 + 3x)12 is -...