Home
Class 12
PHYSICS
if sum(n=1)^oo tan^(-1)(1/(7-5n+n^2))=pi...

if `sum_(n=1)^oo tan^(-1)(1/(7-5n+n^2))=pi/2 +tan^(-1)c` , then c is equal to

A

2

B

3

C

17

D

`5/2`

Text Solution

Verified by Experts

The correct Answer is:
A
`sum_(n=1)^oo tan^(-1)(1/(7-5n+n^2))=sum_(n=1)^oo "tan"^(-1) ((n-2)-(n-3))/(1+(n-2)(n-3))`
`sum_(n=1)^oo[tan^(-1) (n-2)-tan^(-1)(n-3)]`
`=pi/2-tan^(-1)(-2)=pi/2+"tan"^(-1)2=(api)/b + tan^(-1)c`
a=1,b=2,c=2
Promotional Banner

Topper's Solved these Questions

  • SCORE TEST 2

    NEET MAJOR TEST (COACHING)|Exercise PHYSICS|25 Videos

Similar Questions

Explore conceptually related problems

sum_(n=1)^(n)tan^(-1)((n)/(n))

The sum sum_(n=1)^(60)tan^(-1)((2n)/(n^(4)-n^(2)+1)) equals tan^(-1)K, where K equal-

sum_(n=1)^(oo)tan^(-1)((8)/(4n^(2)-4n+1)) is equal to

If x_(0)=sum_(n=1)^(oo)tan^(-1)((4n)/(n^(4)-2n^(2)+3)), then which of the following is/are correct

The value of sum sum_(n=1)^(oo)cot^(-1)(((n^(2)+2n)(n^(2)+2n+1)+1)/(2n+2)) is equal to

NEET MAJOR TEST (COACHING)-TEST 1 -PHYSICS
  1. Two circles with unequal radii,centred at A and B respectively,touch e...

    Text Solution

    |

  2. lim(Nrarroo) sum(r=1)^n (2r-1)/2^r is equal to :-

    Text Solution

    |

  3. lim(Nrarroo) [(1-2sin theta)^nsum(r=0)^n .^nCr((sin 2 theta+sin theta...

    Text Solution

    |

  4. A circle passes through the points of intersection of the parabola y+1...

    Text Solution

    |

  5. Rectangle ABCD has area 200 sq. unit.An ellipse with area 200pi sq.uni...

    Text Solution

    |

  6. if sum(n=1)^oo tan^(-1)(1/(7-5n+n^2))=pi/2 +tan^(-1)c , then c is equa...

    Text Solution

    |

  7. If the equation in x given by (2(1/(cos^(-1)x)))^(2pi)-(a+1/2)(2(1/(co...

    Text Solution

    |

  8. if 'a' is the number of distributions of six different balls into thre...

    Text Solution

    |

  9. Number of points where the function f(x)={{:(max(|x^2-x-2|","x^2-3x)",...

    Text Solution

    |

  10. A triangle has sides of length 6, 7 and 8. The line through its incent...

    Text Solution

    |

  11. Let f be a differentiable function with range (0,oo) and g(x)=(f(x))^2...

    Text Solution

    |

  12. If f(x)max{x^2,(1-x)^2,3/4}, x in [0,1] , then the value of underset0o...

    Text Solution

    |

  13. If a hyperbola centred at origin, has one of its directrix as x=2.Also...

    Text Solution

    |

  14. A survey of 500 television viewers produced the following information,...

    Text Solution

    |

  15. The statement (p to q) ∨ (q to p) is

    Text Solution

    |

  16. Consider four independent trials in which an event A occurs with proba...

    Text Solution

    |

  17. If the mean deviation of the data set 3, 10, 10, 4, 7, 10, 5 from the ...

    Text Solution

    |

  18. In DeltaABC, If angleA=pi/6 , angleB=pi/4 and If (AB)^2 =K(BC)^2 + (AC...

    Text Solution

    |

  19. If 'A' is a square matrix of order 3 x 3 and det(A)=1/2 , then det(Adj...

    Text Solution

    |

  20. Consider the curves C1:y^2=4k1x AA k1 in [1/8,1/4] C2:x^2=4k2(y-2)...

    Text Solution

    |