Home
Class 12
MATHS
If S= tan^(-1) ((1)/(n^(2) +n+1)) + tan^...

If `S= tan^(-1) ((1)/(n^(2) +n+1)) + tan^(-1) ((1)/(n^(2) + 2n+ 3))+ ….+ tan^(-1) ((1)/(1+(n+19) (n+20)))`, then `tan (s)` is equal to

A

`(20)/(401 + 20n)`

B

`(n)/(n^(2) + 20n+1)`

C

`(20)/(n^(2) + 20n+1)`

D

`(n)/(401 + 20n)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    AAKASH SERIES|Exercise Practice Exercise|71 Videos

  • REVISION EXERCISE

    AAKASH SERIES|Exercise STRAIGHT LINES|24 Videos

  • SETS AND RELATIONS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|26 Videos

Similar Questions

Explore conceptually related problems

Tan^(-1) ((1)/( 1+1+1^2) ) + Tan^(-1) ((1)/( 1+2+2^2) ) + ….. + Tan^(-1) ((1)/( 1+ n+n^2) )=

If Y = "tan"^(-1)((1)/(1 + x + x^2)) + "tan"^(-1) (1/(x^2 + 3x + 3)) + "tan"^(-1)(1/(x^2 + 5x + 7)) + ….+ upto n term then y^1(0) =

"tan"^(-1)1/3+"tan"^(-1)1/7+……+tan^(-1)(1/(n^(2)+n+1))=

If y = "Tan"^(-1)((1)/(cos^2 x + cos x + 1)) + "Tan"^(-1)(1/(cos^2x + 3 cos x + 3))+ ….upto n term then f^(1)(0) =

1 ^(2) + 2^(2) + 3^(2) + . . . + n^(2) = (n (n + 1) (2 n + 1))/( 6)

Tan^(-1)(m/n)-Tan^(-1)((m-n)/(m+n))=

If "Tan"^(-1)1/(1+2)+"Tan"^(-1)1/(1+(2)(3))+"Tan"^(-1)1/(1+(3)(4))+..."Tan"^(-1)1/(1+n(n+1))=Tan^(-1)theta , then theta =

For all n in N, x in R, tan^(-1) [ ( x)/( 1.2+ x^2) ] + tan^(-1) [ (x)/( 2.3+ x^2) ] + …. + tan^(-1) [ ( x)/( n(n+1) +x^2) ] =

AAKASH SERIES-SEQUENCE AND SERIES-Practice Exercise
  1. Given sum of the first n terms of an A.P is 2n+ 3n^(2). Another A.P is...

    Text Solution

    |

  2. The sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2)+ 2^(2) + 3^(2))...

    Text Solution

    |

  3. Given a sequence of 4 numbers, first three of which are in G.P.,and th...

    Text Solution

    |

  4. The value of 1^(2) + 3^(2) + 5^(2) + …+ 25^(2) is

    Text Solution

    |

  5. Let a(1), a(2), a(3)….. be terms of an A.P. If (a(1) + a(2) + …..a(p))...

    Text Solution

    |

  6. The sum of the series 2^(2) + 2(4^(2)) + 3(6^(2)) + ….upto 10 terms is

    Text Solution

    |

  7. If S= tan^(-1) ((1)/(n^(2) +n+1)) + tan^(-1) ((1)/(n^(2) + 2n+ 3))+ …....

    Text Solution

    |

  8. If a(1), a(2), a(3),…, a(n) are in A.P such that a(4) - a(7) + a(10)= ...

    Text Solution

    |

  9. Given an A.P whose terms are all positive integers. The sum of its nin...

    Text Solution

    |

  10. If the sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2) + 2^(2) + 3^...

    Text Solution

    |

  11. In a geometric progression, if the ratio of the sum of first 5 terms t...

    Text Solution

    |

  12. The sum of the first 20 terms common between the series 3+7 + 11 + 15…...

    Text Solution

    |

  13. Let G be the geometric mean of two positive numbers a and b, and M be ...

    Text Solution

    |

  14. The lest positive integer n such that 1- (2)/(3)- (2)/(3^(2))- ….- (2)...

    Text Solution

    |

  15. The number of terms in an A.P is even the sum of the odd terms in it i...

    Text Solution

    |

  16. Let f(n)= [(1)/(3) + (3n)/(100)]n, where [n] denotes the greatest inte...

    Text Solution

    |

  17. If the sum of first n terms of two A.P's are in the ratio 3n+8: 7n+15,...

    Text Solution

    |

  18. A tree, in each year grows 5cm less than it grew in the previous year....

    Text Solution

    |

  19. If log(10)2, log(10) (2^(x)-1) and log(10) (2^(x) + 3) are three conse...

    Text Solution

    |

  20. If (48)/((2)(3)) + (47)/((3)(4)) + (46)/((4)(5))+ …..(2)/((48) (49)) +...

    Text Solution

    |