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Consider (1 + x + x^(2))^(n) = sum(r=0)...

Consider `(1 + x + x^(2))^(n) = sum_(r=0)^(n) a_(r) x^(r)` , where ` a_(0), a_(1), a_(2),…, a_(2n)` are
real number and n is positive integer.
The value of ` sum_(r=0)^(n-1) a_(r)` is

A

`(3^(n) - 1 + 2a_(n))/(2)`

B

`(3^(n) - 1 + 2a_(n))/(4)`

C

`(3^(n) + 1 + 2n_(n))/(2)`

D

`(3^(n) + 1 - 2a_(n))/(4)`

Text Solution

Verified by Experts

The correct Answer is:
b
From Eq . (viii), we get
` (3^(n) -1)/(2) = 2 (a_(1) + a_(3) + …+ a_(n)) - a_(n)`
` (3^(n) -1 + 2a_(n))/(4) = (a_(1) + a_(3) + …+ a_(n))`
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ARIHANT MATHS ENGLISH-BIONOMIAL THEOREM-Exercise (Passage Based Questions)
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