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If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+...

If `(1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n)`, then prove that
`a_(1)+a_(3)+a_(5)+….+a_(2n-1)=(3^(n)-1)/(2)`

A

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

B

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

C

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

D

`(2^(n-1))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1B (BINOMIAL COEFFICIENTS)
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  2. The sum of the coefficients of odd powers of x in the expansion of (1+...

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  3. The sum of coefficients of odd powers of x in the expansion of (1+x-x^...

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  4. The sum of coefficients of integral powers of x in the binomial expans...

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  5. Sum of the last 30 coefficients in the expansion of (1+x)^59, when exp...

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  6. If the sum of the coefficients of (x+y)^n is 4096 , then the greatest ...

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  7. If the sum of the coefficients of (1+2x)^n is 6561 then the value of n

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  8. If the sum of the coefficients in the expansion of (1-3x+10x^2)^n is a...

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  9. If (1 -x + x^2)^n = a0 +a1x + a2x^2+….+a(2n)x^(2n) then a0 + a2 +a4 +...

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  10. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  11. If (1+2x+x^2)^n= sum(r=0)^(2n) a, x' then ar=

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  12. If (1+2x +3x^2)^10 = a0 +a1x +a2x^2 + ……+a20x^20 then a2/a1 =

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  13. If (1+x -2x^2)^8 =1 -a1x + a2x^2+……+a16x^16, then a2+a4+a6+……+a16 =

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  14. If (1+x+x^2+x^3)^5=sum(k=0)^(15) ak x^k then sum(k=0)^(7) a24=

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  15. If ak is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k...

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  16. If (3 + 7x - 9x^2)^n = a0 +a1x + a2 x^2 + ……+a(2n)x^(2n) prove the a0 ...

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  17. If (1+x+x^2)^n = sum(r=0)^(2n) ar x' then a1-2a2 + 3a3-…..-2na(2n)=….....

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  18. If ar is the coefficient of x^r in the expansion of (1-2x+3x^2)^n then...

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  19. If the sum of the coefficient in the expansion of (p^2 x^2 - 2px+1)^51...

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  20. If the number of terms in the expansion of (1-(2)/(x)+(4)/(x^2))^n, ...

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