Home
Class 12
MATHS
The sum of the series (1)/(2!)+(1)/(4!)+...

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

A

`(e^(2)-2)/(e )`

B

`(e-1)^(2)/(2e)`

C

`(e^(2)-1)/(2e)`

D

`(e^(2)-1)/(2)`

Text Solution

AI Generated Solution

To find the sum of the series \( S = \frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \ldots \) to infinity, we can use the properties of the exponential function. ### Step-by-Step Solution: 1. **Recall the Exponential Series**: The exponential function \( e^x \) can be expressed as: \[ e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots ...
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 sum of the series (1)/(2!)+(1+2)/(3!)+(1+2+3)/(4!)+..to infty is equal to

The sum of the series (1)/(1.23)+(1)/(3.45)+(1)/(5.67)+…infty is

The sum of the series 1/(2!)-1/(3!)+1/(4!)-... upto infinity is (1) e^(-2) (2) e^(-1) (3) e^(-1//2) (4) e^(1//2)

The sum of the series 1+(1)/(4)+(1)/(16)+(1)/(64)+....oo is

The sum of the series (1)/(2!)-(1)/(3!)+(1)/(4!)-(1)/(5!) +….up to infty is

Statement -1: The sum of the series (1)/(1!)+(2)/(2!)+(3)/(3!)+(4)/(4!)+..to infty is e Statement 2: The sum of the seies (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3)+(4)/(4!)x^(4)..to infty is x e^(x)

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

The sum of the series (2)/(1!) + (4)/(3!) + (6)/(5!) + ……. "to" oo equals

The sum of the series 1 + (1)/(1!) ((1)/(4)) + (1.3)/(2!) ((1)/(4))^(2) + (1.3.5)/(3!) ((1)/(4))^(3)+ ... to infty , is

The sum of the series (1)/(1!)x+(2)/(2!)x^(2)+(3)/(3!)x^(3) ….. To infty 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

    |