Home
Class 11
MATHS
Sum of infinite terms of the series cot^...

Sum of infinite terms of the series `cot^(-1)(1^(2)+3/4)+cot^(-1)(2^(2)+3/4)+cot^(-1)(3^(2)+3/4)+…..` is

A

`pi/4`

B

`tan^(-1)2`

C

`tan^(-1)3`

D

`tan^(-1)4`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - II) (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS)|4 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - II) (MATRIX MATCHING TYPE QUESTIONS)|1 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - I DOMAIN, RANGE, PRINCIPAL VALUES, BASIC PROPERTIES) (INTEGER TYPE QUESTIONS)|5 Videos

  • HYPERBOLIC FUNCTIONS

    AAKASH SERIES|Exercise PRACTICE SHEET EXERCISE-II (STRAIGHT OBJECTIVE TYPE QUESTIONS)|18 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|37 Videos

Similar Questions

Explore conceptually related problems

The sum of infinite terms of the series cot^(-1)(2^(2)+1/2)+cot^(-1)(2^(3)+1/2^(2))+cot^(-1)(2^(4)+1/2^(3))+…=cot^(-1)k then k =

Find the value of the following cot^(-1)(1/2)+cot^(-1)(1/3)

Cot^(-1)(4/3)-Cot^(-1)(15/8)=

cot((pi)/4-2cot^(-1)3)=

The sum of n terms of the series 1^(2) - 2^(2) + 3^(2)- 4^(2) + 5^(2) -6^(2) + ….is

tan h^(-1)""(1)/(2)+ cot h^(-1) 3=

The sum of the series (1)/(2)((1)/(5))^(2)+(2)/(3)((1)/(5))^(3)+(3)/(4)((1)/(5))^(4)+... is

If S_(n)=cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+cot^(-1)(21)+….. n terms, then

tan^(-1)3+"cot"^(-1)3=(pi)/2

AAKASH SERIES-INVERSE TRIGNOMETRIC FUNCTIONS-LECTURE SHEET (EXERCISE - II) (STRAIGHT OBJECTIVE TYPE QUESTIONS)
  1. If we consider only the principle values of the inverse trigonometric ...

    Text Solution

    |

  2. Find the value of tan(2"Tan"^(-1)(1/5)-(pi)/4)

    Text Solution

    |

  3. If x,y,z are in A.P and Tan^(-1) x, Tan^(-1) y and Tan^(-1) z are als...

    Text Solution

    |

  4. Cot^(-1)(sqrt(Cos alpha))-Tan^(-1)( sqrt(Cos alpha))=x then Sinx=

    Text Solution

    |

  5. The number of solutions of the equation Tan^(-1)(x-1)+Tan^(-1)(x+1)=Ta...

    Text Solution

    |

  6. The value of tan[Tan^(-1)(1/(a+b))+Tan^(-1)(b/(a^(2)+ab+1))] is

    Text Solution

    |

  7. The arithmetic mean of the non-zero solutions of the equation "Tan"^...

    Text Solution

    |

  8. If a,b,c, are positive then tan^(-1)sqrt((a(a+b+c))/(bc))+tan^(-1)sq...

    Text Solution

    |

  9. If alpha, beta, gamma are the roots of the equation x^(3)+mx^(2)+3x+m=...

    Text Solution

    |

  10. If Cos^(-1)x-Cos^(-1)(y/2)=alpha" then "4x^(2)-4xycosalpha+y^(2)=

    Text Solution

    |

  11. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/z then the value of sum((x^(201...

    Text Solution

    |

  12. If Cos^(-1)x+Cos^(-1)y+Cos^(-1)z=pi,"then "x^(2)+y^(2)+z^(2)+2xyz=

    Text Solution

    |

  13. The value of alpha such that sin^(-1)""2/sqrt(5), sin^(-1)""3/sqrt(10)...

    Text Solution

    |

  14. sum(r=1)^(n)sin^(-1)((sqrt(r)-sqrt(r-1))/sqrt(r(r+1))) is equal to

    Text Solution

    |

  15. sum(m=1)^(oo)Tan^(-1) ((2m)/(m^(4)+m^(2)+2))=

    Text Solution

    |

  16. The value of "tan"^(-1)4/7+"tan"^(-1)4/19+"tan"^(-1)4/39+"tan"^(-1)4/6...

    Text Solution

    |

  17. The sum of series sec^(-1)sqrt(2)+"sec"^(-1)(sqrt(10))/3+"sec"^(-1)(sq...

    Text Solution

    |

  18. Sum of infinite terms of the series cot^(-1)(1^(2)+3/4)+cot^(-1)(2^(2)...

    Text Solution

    |

  19. Tan^(-1)(1/3)+Tan^(-1)(2/9)+Tan^(-1)(4/33)+…… infty

    Text Solution

    |

  20. The value of cot(sum(n=1)^(23)cot^(-1)(1+sum(k=1)^(n)2k)) is

    Text Solution

    |