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The sum of the series ((a-b)/(a))+1/2(...

The sum of the series
`((a-b)/(a))+1/2((a-b)/(x))^(2)+1/3((a-b)/(a))^(3)+….infty` is

A

log ab

B

`log ((b)/(a))`

C

`log ((a)/(b))`

D

`log a^(b)`

Text Solution

Verified by Experts

The correct Answer is:
C
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ML KHANNA-EXPONENTIAL AND LOGARITHMIC SERIES -Problem Set (2) (MULTIPLE CHOICE QUESTIONS )
  1. The sum of the series ((a-b)/(a))+1/2((a-b)/(x))^(2)+1/3((a-b)/(a))^...

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  2. e^((x-1)-(1)/(2) (x-1)^(2) + (1)/(3) (x-1)^(3) - (1)/(4) (x-1)^(4) +.....

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  3. If y = x - (x^(2))/(2) + (x^(3))/(3) -... then x =

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  4. The sum of the series log(4) 2 -log(8) 2 + log(16) 2 -...is

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  5. If S = (1)/(1.2) - (1)/(2.3) + (1)/(3.4) -(1)/(4.5) +...oo

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  6. The sum of the series (1)/(2.3) + (1)/(4.5) + (1)/(6.7) + ...oo=

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  7. (1)/(1.3) + (1)/(2.5) + (1)/(3.7) + (1)/(4.9) +... is equal to

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  8. 1 + (2)/(1.2.3) + (2)/(3.4.5) + (2)/(5.6.7) + ... =

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  9. 1 /(1.3.5) + (1)/(3.5.7) + (1)/(5.7.9) +...oo

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

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

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

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

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  15. 2[(1)/(2x + 1) + (1)/(3(2x + 1)^(3)) + (1)/(5(2x + 1)^(5)) + (1)/(5(2x...

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

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

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

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  20. 2log x-log(x+1)-log(x-1) is equals to

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