Home
Class 12
MATHS
The value of 1+(log(e)x)+(log(e)x)^(2)...

The value of
`1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty`

A

`log_(e)x`

B

`-log_(e)x`

C

`2log_(e)x`

D

x

Text Solution

AI Generated Solution

To solve the given series \[ 1 + \frac{(\log_e x)}{1!} + \frac{(\log_e x)^2}{2!} + \frac{(\log_e x)^3}{3!} + \ldots \] we can recognize that this series resembles the Taylor series expansion for the exponential function \( e^x \), which is given by: ...
Promotional Banner

Topper's Solved these Questions

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|37 Videos

  • EXPONENTIAL AND LOGARITHMIC SERIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|20 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • HEIGHTS AND DISTANCES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

Similar Questions

Explore conceptually related problems

The value of 1-log_(e)2+(log_(e)2)^(2)/(2!)-(log_(e)2)^(3)/(3!)+.. is

Let x and a be positive real numbers Statement 1: The sum of theries 1+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+(log_(e)x)^(2)+…to infty is x Statement2: The sum of the series 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)x))^(2)+(x^(3))/(3!)(log_(e)a)^(3)/(3!)+to infty is a^(x)

The value of x, log_(1/2)x >= log_(1/3)x is

1+(log_(e)5)/(1!) +(log_e5)^2/(2!)+(log_e5)^3/(3!)+ .......oo =

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

If agt0 and x in R , then 1+(xlog_(e)a)+(x^(2))/(2!)(log_(e)a)^(2)+(x^(3))/(3!)(log_(e)a)^(3)+….infty is equal to

The value of lim_(xrarr3) ((x^(3)+27)log_(e)(x-2))/(x^(2)-9) is

Find the range of f(x)=log_e x-((log_e x)^2)/(|log_e x|).

int (dx)/(x(1+log_(e)x)(3+log_(e)x))

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is

OBJECTIVE RD SHARMA ENGLISH-EXPONENTIAL AND LOGARITHMIC SERIES-Section I - Solved Mcqs
  1. In the expansion of log(10)(1-x),|x|lt1 the coefficient of x^(n) is

    Text Solution

    |

  2. Sum of series 9/(1!)+19/(2!)+35/(3!)+57/(4!)+... (A) 7e-3 (B) 12e-5...

    Text Solution

    |

  3. The constant term in the expansion of (3^(x)-2^(x))/(x^(2)) is

    Text Solution

    |

  4. Sigma(n=1)^(oo) (x^(2n))/(2n-1) is equal to

    Text Solution

    |

  5. Then sum of the series 1+(1+3)/(2!)x+(1+3+5)/(3!)x^(2)+(1+3+5+7)/(4...

    Text Solution

    |

  6. 1/(e^(3x))(e^x+e^(5x))=a0+a1x+a2x^2+........=>2a1+2^3a3+2^5a5+......=

    Text Solution

    |

  7. Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C=1-(x^(2))/(2!)+(x^(4))/(4!) T...

    Text Solution

    |

  8. The sum of series 2/(3!)+4/(5!)+6/(7!)+...........oo is :

    Text Solution

    |

  9. The sum of the series S=Sigma(n=1)^(infty)(1)/(n-1)! is

    Text Solution

    |

  10. The sum of the series loge(3)+(loge(3))^3/(3!)+(loge(3))^5/(5!)+....+ ...

    Text Solution

    |

  11. The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...

    Text Solution

    |

  12. (1+3)loge3+(1+3^2)/(2!)(loge3)^2+(1+3^3)/(3!)(loge 3)^3+....oo= (a)28...

    Text Solution

    |

  13. If agt0 and x in R, then 1+(xlog(e)a)+(x^(2))/(2!)(log(e)a)^(2)+(x^(...

    Text Solution

    |

  14. (2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+….infty is equal to

    Text Solution

    |

  15. 1+(2x)/(1!)+(3x^(2))/(2!)+(4x^(3))/(3!)+..infty is equal to

    Text Solution

    |

  16. 1/2(1/2+1/3)-1/4((1)/(2^(2))+(1)/(3^(2)))+1/6((1)/(2^(3))+(1)/(3^(3)))...

    Text Solution

    |

  17. The sum of series (1)^(2)/(1.2!)+(1^(2)+2^(2))/(2.3!)+(1^(2)+2^(2)+3...

    Text Solution

    |

  18. The sum of the series (1)/(2!)+(1)/(4!)+(1)/(6!)+..to infty is

    Text Solution

    |

  19. If 0ltylt2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)/(5x...

    Text Solution

    |

  20. The sum of the series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+..to infty is...

    Text Solution

    |