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If ( 1 + x - 2x^(2))^(20) = sum(r=0)^(4...

If ` ( 1 + x - 2x^(2))^(20) = sum_(r=0)^(40) a_(r) x^(r) ` , then find
the value of ` a_(1) + a_(3) + a_(5) + …+ a_(39)` .

A

`2^(19) (2^(19- 20)`

B

`2^(19) (2^(20) - 21)`

C

`2^(19) (2^(19) - 21)`

D

`2^(19) (2^(19) -19)`

Text Solution

Verified by Experts

The correct Answer is:
b
` a_(1) + a_(2) + a_(4) + …+ a_(38) + a_(40) = 2^(19) (2^(20) + 1) " " ` [from Eq. (iii) ]
` rArr a_(0) + a_(2) + a_(4) + …+ a_(38) = 2^(19) (2^(20) +1) - a_(40) `
` = 2^(19) (2^(20) + 1) - 2^(20) " " ` [ From Eq . (vi)]
` = 2^(19) (2^(20) -1) `
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