Home
Class 12
MATHS
Statement-I : ((x-y)/(x))+(1)/(2)((x-y...

Statement-I :
`((x-y)/(x))+(1)/(2)((x-y)/(x))^(2)+(1)/(3)((x-y)/(x))^(3)+….=log_(e )x-log_(e )y`
Statement-II :
`(a-1)-((a-1)^(2))/(2)+((a-1)^(3))/(3)-((a-1)^(4))/(4 )+….=log_(e )a`
Which of the above statements true

A

Only I

B

Only II

C

both I & II

D

neither I nor II

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • LOGARITHMIC SERIES

    AAKASH SERIES|Exercise EXERCISE - II(B) (HOME WORK)|30 Videos

  • LOGARITHMIC SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos

  • LOGARITHMIC SERIES

    AAKASH SERIES|Exercise EXERCISE - I(B) (HOME WORK)|9 Videos

  • INDEFINITE INTEGRALS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|167 Videos

  • MATHEMATICAL REASONING

    AAKASH SERIES|Exercise Practice Exercise|21 Videos

Similar Questions

Explore conceptually related problems

A : (a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/(a))^(3)+....=log_(e)((a)/(b)) R : log_(e)(1-x)=-x-(x^(2))/(2)-(x^(3))/(3)-(x^(4))/(4)-....

Statement-I : If (3x+4)/((x+1)^(2)(x-1))=(A)/(x-1)+(B)/(x+1)+(C)/((x+1)^(2)) then A=7//4 Statement-II : If (px+q)/((2x-3)^(2))=(1)/(2x-3)+(3)/((2x-3)^(2)) then p=2, q=3 . Which of the above statements is true

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

Statement-I : log(1+x+x^(2)+…)=x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)+… Statement-II : 4^(th) term of log(3//2) is (-1)/(64) Statement-III: "Tan"^(2)x-(1)/(2)"Tan"^(4)x+(1)/(3)"Tan"^(6)x ………. =2log(sec x) Which of the above statements are true

Statement I : (2x-1)/((x+1)(x^(2)+2))=(A)/(x+1)+(3x+c)/(x^(2)+2) then A= -1 Statement II : (Ax)/((x+2)(2x-3))=(2)/(x+2)+(3)/(2x-3) then A= 7 Statement III : The number of partial fractions of (x^(2)+1)/((x-1)^(4)) is 3. Which of the above statements are true.

lim_(x to 0) {(log_(e)(1+x))/(x^(2))+(x-1)/(x)}=

1+2(log_(e)a)+(2^(2))/(2!)(log_(e)a)^(2)+(2^(3))/(3!)(log_(e)a)^(3)+....=

1+x(log_(e)2)+(x^(2))/(2!)(log_(e)2)^(2)+(x^(3))/(3!)(log_(e)2)^(3)+....=

Assertion (A) : (1)/(5)+(1)/(3.5^(3))+(1)/(5.5^(5))+(1)/(7.5^(7))+…(1)/(2)log((3)/(2)) Reason (R ) : If |x| lt 1 then log_(e )((1+x)/(1-x))=2(x+(x^(3))/(3)+(x^(5))/(5)+…)

AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. y=2x^(2)-1, then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…….oo

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. (1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

    Text Solution

    |

  8. 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If 0 lt y lt 1, then sum(n=1)^(oo)(1)/(2n-1)*y^(n+1)=……

    Text Solution

    |

  15. If log(e )((1+x)/(1-x))=a(0)+a(1)x+a(2)x^(2)+…oo then a(1), a(3), a(5)...

    Text Solution

    |

  16. Assertion (A) : The coefficient of of x^(5) in the expansion log(e ) (...

    Text Solution

    |

  17. If n is a multiple of 3, then coefficient of x^(n) in log(1+x+x^(2)) i...

    Text Solution

    |

  18. If n is a not a multiple of 3, then the coefficient of x^(n) in the ex...

    Text Solution

    |

  19. Match the following for coefficient of x^(n) in log(e )(1+x+x^(2)) ...

    Text Solution

    |

  20. If |x|lt1, the coefficient of x^(3) in the expansion of log(1+x+x^(2))...

    Text Solution

    |