Home
Class 12
MATHS
If |x| lt 1 then coefficient of x^(n) in...

If `|x| lt 1` then coefficient of `x^(n)` in `log_(10)(1-x)` is

A

`-(1)/(n)`

B

`-(1)/(n) log_(10 )e`

C

`(1)/(n)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
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

Coefficient of x^(2) in log(1+x) =

If |x| lt 1 then coefficient of x^(2) in (log(1+x))/((1-x)^(2)) is

Coefficient of x^(n) in log_(e )(1+(x)/(2)) is

The coefficient of x^(n) in (1)/((1-2x)(1-3x)) is

The coefficient of x^(3) in log(1-5x+6x^(2)) is

Assertion (A) : coefficient x^(n) in log(1+x) is ((-1)^(n-1))/(n) when |x| lt 1 . Reason (R ) : Coefficient of x^(n) in log(1-x) is -1//2 when |x| lt 1 .

The coefficient of x^(-n) in (1+x)^n (1+(1)/(x))^n is

The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. sum(n=1)^(oo)(1)/(2n(2n+1))=

    Text Solution

    |

  2. -2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. (1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

    Text Solution

    |

  16. 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |