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If log(1-x+x^(2))=a(1)x+a(2)x^(2)+a(3)x^...

If log`(1-x+x^(2))=a_(1)x+a_(2)x^(2)+a_(3)x^(3)+…`
then `a_(3)+a_(6)+a_(9)+..` is equal to

A

`(1)/(n)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
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ML KHANNA-EXPONENTIAL AND LOGARITHMIC SERIES -Problem Set (2) (MULTIPLE CHOICE QUESTIONS )
  1. 1 /(1.3.5) + (1)/(3.5.7) + (1)/(5.7.9) +...oo

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  2. Sum of the series 1/(1*2*3)+5/(3*4*5)+9/(5*6*7 )+... is equal to

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  3. Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+.....

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  4. If y+(y^(3))/(3)+(Y^(5))/(5)+…infty=2(x+(x^(3))/(3)+(x^(5))/(5)+..inft...

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  5. The coefficient of x^(n) in the exansion of log(e)(1+3x+2x^(2)) is

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  6. The value of log 2+2 (1/5+1/3.(1)/(5^(3))+1/5.(1)/(5^(5))+..+infty) is

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  7. 2[(1)/(2x + 1) + (1)/(3(2x + 1)^(3)) + (1)/(5(2x + 1)^(5)) + (1)/(5(2x...

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  8. 2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5)+..} is equals ...

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  9. The sum of the series 1 + ((1)/(2) + (1)/(3)) (1)/(4) + ((1)/(4) + ...

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  10. The series expansion of log{(1+x)^(1+x)(1-x)^(1-x)} is

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  11. The coefficient of x^(6) in the expansion of log{(1+x)^(1+x)(1-x)^(...

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  12. 2log x-log(x+1)-log(x-1) is equals to

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  13. The coefficient of x^(n), where n = 3k in the expansion of log (1 + x ...

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  14. The coefficient of x^(n) in the expansion of log(e)((1)/(1+x+x^(2)+x^(...

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  15. If log(1-x+x^(2))=a(1)x+a(2)x^(2)+a(3)x^(3)+… then a(3)+a(6)+a(9)+.....

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  16. The coefficient of n^(-r) in the expansion of log(10)((n)/(n-1)) is

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  17. If log(1-x+x^(2))=a(1)x+a(2)x^(2)+a(3)x^(3)+… then a(3)+a(6)+a(9)+.....

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  18. The sum of the series (1)/(2)x^(2) + (2)/(3)x^(3) + (3)/(4)x^(4) + ...

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  19. If x, y, z are three consecutive positive integers, then (1)/(2) log...

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  20. If S =(y-1-1/2(y-1)^(2)+1/3(y-1))^(3)/(a-1-1/2(a-1)^(2)+1/3(a-1)^(3)…....

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