Home
Class 12
MATHS
Find the sum of each of the following se...

Find the sum of each of the following series :(i) `tan^-1(1/(x^2+x+1))+tan^-1 (1/(x^2+3x+3))+tan^-1(1/(x^2+5X+7))+tan^-1(1/x^2+7x+13))`......upto n.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Solve tan^-1(1/(1+2x))+tan^-1(1/(1+4x))=tan^-1(2/x^2)

tan^(- 1) (1/(x+y)) +tan^(- 1) (y/(x^2+x y+1)) =cot^(- 1)x

Sum the series tan^-1 (x/(1+1*2x^2))+tan^-1 (x/(1+2*3x^2))+…+tan^-1 (x/(1+n*(n+1)x^2))

If y = tan^(-1) ((1)/(x^(2) + x + 1)) + tan^(-1) ((1)/( x^(2) + 3x + 3)) + tan^(-1) ((1)/( x^(2) + 5x + 7))+ tan^(-1) ((1)/( x^(2) +7x + 13)), x gt 0 and ((dy)/( dx))_(x=0)= ( - k )/( 1+ k) then the value of k is

Solve : tan^(-1)((x+1)/(x-1)) + tan^(-1)( (x-1)/(x)) = pi + tan^(-1) (-7)

Solve : tan^(-1) x + tan^(-1)( (2x)/(1-x^2)) = pi/3

Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2))

Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2))

tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=pi/4. find X

Solve: tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36))

ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

    Text Solution

    |

  2. Prove that cot^(-1)(13)+cos^(-1)(21)+cot^(-1)(-8)=pi.

    Text Solution

    |

  3. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

    Text Solution

    |

  4. Find the domain of definition the following function: f(x)=log(10)(1-l...

    Text Solution

    |

  5. Simplify : tan ^(−1)(1/2)+tan ^(−1) (1/3).

    Text Solution

    |

  6. Prove that the identities, sin^-1 cos(sin^-1x)+cos^-1 sin(cos^-1x)=pi...

    Text Solution

    |

  7. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=pi/4

    Text Solution

    |

  8. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

    Text Solution

    |

  9. If sin^(-1) x = sin^(-1) y + sin^(-1) z = pi " , prove that " x^(4) + ...

    Text Solution

    |

  10. If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > ...

    Text Solution

    |

  11. Solution set of inequality (cot^-1x)^2-5cot^-1x+6>0 is (A) (cot 3 ,...

    Text Solution

    |

  12. Solve the following inequality: sin^(-1) x > cos^(-1) x

    Text Solution

    |

  13. Solve the following system of inequations: 4(tan^(-1)x)^2-8tan^(-1)x+3...

    Text Solution

    |

  14. Find the number of positive integral solution of the equation tan^(-1)...

    Text Solution

    |

  15. Find all values of k for which there is a triangle whose angles have m...

    Text Solution

    |

  16. Find the range of the function f(x)=(sin^(-1)x)^3+(cos^(-1)x)^3dot

    Text Solution

    |

  17. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

    Text Solution

    |

  18. Thee value of cos ^(−1 )x+cos ^(−1)( x/2​ + root(3-x^2)/2−x2 ​ ), wh...

    Text Solution

    |

  19. The number of solutions of the equation |y|= cos x and y = cot^-1 (cot...

    Text Solution

    |

  20. Solve sin^(-1)[((2x^2+4)/(1+x^2))]<pi-3

    Text Solution

    |