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log(1+x+x^(2)+...oo)=...

`log(1+x+x^(2)+...oo)=`

A

`x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)+…oo`

B

`x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+…oo`

C

`1+x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)+….oo`

D

`1-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+…oo`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. -2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=

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  2. If |x| lt 1 then coefficient of x^(n) in log(10)(1-x) is

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  3. log(1+x+x^(2)+...oo)=

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  4. (2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=

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  5. (sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=

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  6. Assertion (A) : If x+(x^(2))/(2)+(x^(3))/(3)+………oo=log((7)/(6)) then...

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  7. If f(x)=(1)/(x+1)+(1)/(2(x+1)^(2))+(1)/(3(x+1)^(3))+…(x gt 1) and f(1...

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  8. y=2x^(2)-1, then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…….oo

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  9. If |a| lt 1, b = sum(k=1)^(oo) (a^(k))/(k) rArr a=

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  10. If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)...

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  11. Statement-I : ((x-y)/(x))+(1)/(2)((x-y)/(x))^(2)+(1)/(3)((x-y)/(x))^...

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  12. Statement-I : log(1+x+x^(2)+…)=x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)...

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  13. Observe the following lists {:("List-I","List-II"),((A) 1-(1)/(2)+(...

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  14. (1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

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  15. 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

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  16. If y+(y^(3))/(3)+(y^(5))/(5)+…oo=2[x+(x^(3))/(5)+(x^(5))/(5)+…oo] then

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  17. sin2theta+(1)/(3)sin^(3)2theta+(1)/(5)sin^(5)2theta+....=

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  18. If 0 lt y lt 2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)...

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

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  20. sum(n=1)^(oo)(1)/(2n-1)*x^(2n)=

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