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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.
If n is odd , the value of ` sum_(r-1)^(2) a_(2r -1)` 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-BIONOMIAL THEOREM-Exercise (Passage Based Questions)
  1. Consider (1 + x + x^(2))^(n) = sum(r=0)^(n) a(r) x^(r) , where a(0),...

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

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  3. Consider (1 + x + x^(2))^(n) = sum(r=0)^(n) a(r) x^(r) , where a(0),...

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  4. If (1 + x+ 2x^(2))^(20) = a(0) + a(1) x + a(2) x^(2) + …+ a(40) x^(40)...

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  5. If (1 + x+ 2x^(2))^(20) = a(0) + a(1) x + a(2) x^(2) + …+ a(40) x^(40)...

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  6. If (1 + x+ 2x^(2))^(20) = a(0) + a(1) x + a(2) x^(2) + …+ a(40) x^(40)...

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  7. Suppose ,m divided by n , then quotient q and remainder r {:("n)m(q"...

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  8. Suppose ,m divided by n , then quotient q and remainder r {:("n)m(q...

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  9. Suppose ,m divided by n , then quotient q and remainder r {:("n)m(q...

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  10. Consider the binomial expansion of R = (1 + 2x )^(n) = I + f , where...

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  11. Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where...

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  12. Consider the binomial expansion of R = (1 + 2x )^(n) = I = f , where...

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  13. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-1...

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  14. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-1...

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  15. If (x + a(1)) (x + a(2)) (x + a(3)) …(x + a(n)) = x^(n) + S(1) x^(n-1...

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  16. A= (5/2+x/2)^n, B=(1+3x)^m Sum of coefficients of expansion of B is ...

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  17. Sum of coefficients of expansion of B is 6561 . The difference of t...

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  18. Sum of coefficients of expansion of B is 6561 . The difference of t...

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  19. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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  20. Let us consider the binomial expansion (1 + x)^(n) = sum(r=0)^(n) a(...

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