Home
Class 12
MATHS
Prove that underset(r =1) overset(n) sum...

Prove that `underset(r =1) overset(n) sum tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)`

A

` tan^(-1)(2^(n))`

B

` tan^(-1)(2^(n))- (pi)/(4) `

C

` tan^(-1)(2^(n+1))`

D

` tan^(-1)(2^(n+1))- (pi)/(4) `

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|15 Videos

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise JEE MAIN ( ARCHIVE)|12 Videos

  • INVERSE TRIGONOMETRY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|10 Videos

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

  • JEE MAIN - 5

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|5 Videos

Similar Questions

Explore conceptually related problems

Prove that sum_(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(-1) (2^(n)) - (pi)/(4)

Find the value of underset(r = 0) overset(oo)sum tan^(-1) ((1)/(1 + r + r^(2)))

If n is a positive integer, prove that underset(r=1)overset(n)sumr^(3)((""^(n)C_(r))/(""^(n)C_(r-1)))^(2)=((n)(n+1)^(2)(n+2))/(12)

Find the sum sum_(r =1)^(oo) tan^(-1) ((2(2r -1))/(4 + r^(2) (r^(2) -2r + 1)))

underset(r=1)overset(n-1)(sum)cos^(2)""(rpi)/(n) is equal to

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset(10)sum tan^(-1) ((r)/(s))

Prove that sum_(r = 1)^(n+1) (2^(r +1) C_(r - 1) )/(r (r + 1)) = (3^(n+2) - 2n - 5)/((n+1)(n+2))

underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-n^(2)) is equal to

underset(r=0)overset(n)(sum)(-1)^(r).^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+(15^(r))/(2^(4r))+ . . .m" terms"]=

VMC MODULES ENGLISH-INVERSE TRIGONOMETRY-LEVEL-2
  1. Total number of ordered pairs (x, y) satisfying |y| = cos x and y = si...

    Text Solution

    |

  2. Prove that underset(r =1) overset(n) sum tan^(-1) ((2^(r -1))/(1 + 2^(...

    Text Solution

    |

  3. Range of the function f (x) = cos^-1 (-{x}), where {.} is fractional ...

    Text Solution

    |

  4. underset(m =1)overset(n)sum tan^(-1) ((2m)/(m^(4) + m^(2) + 2)) is equ...

    Text Solution

    |

  5. The number of real solutions (x, y), where |y| = sin x, y = cos^-1 (co...

    Text Solution

    |

  6. If f(x)=cos^(- 1)x+cos^(- 1){x/2+1/2sqrt(3-3x^2)}then

    Text Solution

    |

  7. Consider the system of equations cos^(-1)x + (sin^(-1) y)^(2) = (p pi^...

    Text Solution

    |

  8. Let f(x) =e^(cos^(-1)sin(x+pi/3))then

    Text Solution

    |

  9. If tan^-1 y=4 tan^-1x, then y is infinite if

    Text Solution

    |

  10. The sum of the infinite terms of the series "tan"^(-1)((1)/(3))+ "tan...

    Text Solution

    |

  11. If sin^-1x+sin^-1y+sin^-1z=(3pi)/2 and f(1)=2. f(p+q)=f(p). f(q)AAp,q...

    Text Solution

    |

  12. If the mapping f(x) = mx + c, m gt 0 maps [-1,1] onto [0,2], then t...

    Text Solution

    |

  13. Statement 1: tan^(-1)((3)/(4))+tan^(-1)((1)/(7))=(pi)/(4) Statement ...

    Text Solution

    |

  14. Statement 1: The value of cot^(-1)((7)/(4))+cot^(-1)((19)/(4))+...+cot...

    Text Solution

    |

  15. Statement 1: If x=(1)/(5 sqrt(2)), then [x cos(cot^(-1)x)+sin(cot^(-1)...

    Text Solution

    |

  16. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

    Text Solution

    |

  17. The sum of the series to infinity cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^...

    Text Solution

    |

  18. If lim(n to oo) sum(k=2)^(n)cos^(-1)((1+sqrt((k-1)(k+2)(k+1)k))/(k(k+...

    Text Solution

    |

  19. Number of solutions of the equation tan^(-1)((1)/(a-1))=tan^(-1)((1)/...

    Text Solution

    |

  20. The sum of the infinite series cot^(-1)((7)/(4))+cot^(-1)((19)/(4))+co...

    Text Solution

    |