Home
Class 12
MATHS
Find the sum of infinite series s = si...

Find the sum of infinite series
`s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ((sqrt2 -1)/sqrt6) + sin ^(-1) ((sqrt3 - sqrt2)/(2sqrt3)) + ...+ sin^(-1) ((sqrtn - sqrt(n-1))/(sqrt(n(n+1))))+... infty`

Text Solution

Verified by Experts

The correct Answer is:
`(pi)/2`
NA
Promotional Banner

Topper's Solved these Questions

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SCQ_TYPE|96 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise MATCH THE COLUMN|2 Videos

  • RELATION, FUNCTION & ITF

    RESONANCE ENGLISH|Exercise SSP|55 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

  • SEQUENCE & SERIES

    RESONANCE ENGLISH|Exercise EXERCISE -2 (PART-II : PREVIOUSLY ASKED QUESTION OF RMO)|3 Videos

Similar Questions

Explore conceptually related problems

The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+....sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))

The sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(2)-1)/(sqrt(6)))+....sin^(-1)((sqrt(n)-sqrt(n-1))/(sqrt(n(n+1))))

sin^(-1)(1/2)-2sin^(-1)(1/(sqrt(2)))

1/(sqrt3 + sqrt2) + 1/(sqrt3 -sqrt2)=

1. sin^(-1)((1)/(sqrt(2))) 2. cos^(-1)((sqrt(3))/(2))

The value of sin ^(-1) (-(1)/(sqrt2)) + cos ^(-1) (-(1)/(2)) - tan ^(-1) (-sqrt3) + cot ^(-1) (-(1)/(sqrt3)) is

Find the value of : sin^(-1) (sqrt(3)/2)

Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))

Evaluate : sin^-1 (- sqrt(3)/2)

The value of sin^-1 (sqrt(3)/2)+ sin^-1 (1/sqrt(2)) is equal to (A) sin^-1 ((sqrt(3+1))/(2sqrt(2))) (B) pi-sin^-1 ((sqrt(3+1))/(2sqrt(2))) (C) pi+sin^-1 ((sqrt(3+1))/(2sqrt(2))) (D) none of these

RESONANCE ENGLISH-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
  1. Find the value of sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x))

    Text Solution

    |

  2. tan^(-1)x + cot^(-1) (1/x) + 2tan^(-1)z =pi, then prove that x + y + 2...

    Text Solution

    |

  3. If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cosec^(-1)z,...

    Text Solution

    |

  4. Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x...

    Text Solution

    |

  5. Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1...

    Text Solution

    |

  6. Express in terms of : "tan"^(-1)(2x)/(1-x^(2) to tan^(-1)x for xgt1

    Text Solution

    |

  7. sin^(-1)(2xsqrt(1-x^2)),x in [1/sqrt2,1] is equal to

    Text Solution

    |

  8. Express in terms of : cos^(-1)(2x^(2)-1) to cos^(-1)x for -1lexlt0

    Text Solution

    |

  9. Find the value of tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1...

    Text Solution

    |

  10. Solve for x : cos(2sin^(-1)x)=1/3

    Text Solution

    |

  11. Solve for x : cot^(-1)x+tan^(-1)3=(pi)/2

    Text Solution

    |

  12. Solve : tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=pi/4

    Text Solution

    |

  13. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

    Text Solution

    |

  14. Prove that : sin^(-1)8/(17)+sin^(-1)3/5=sin^(-1)(77)/(85)=tan^(-1)((77...

    Text Solution

    |

  15. Prove that : "tan"^(-1)3/4+"sin"^(-1)5/13="cos"^(-1)33/65

    Text Solution

    |

  16. Prove: sin^(-1)(1/sqrt5)+cot^(-1)3=pi/4

    Text Solution

    |

  17. Prove that : tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=p...

    Text Solution

    |

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

    Text Solution

    |

  19. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

    Text Solution

    |

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

    Text Solution

    |