Home
Class 12
MATHS
If S(r) = sqrt(r+sqrt(r+sqrt(r+sqrt(r+.....

If `S_(r) = sqrt(r+sqrt(r+sqrt(r+sqrt(r+.....oo)))),r gt 0,` then which of the following is/are correct.

A

`S_(2), S_(6), S_(13), S _(20) ` are in A.P.

B

`S_(4), S_(9), S_(16)` are irrational

C

`(2S_(3)-1) ^(2), (2S_(4)-1)^(2) , (2S_(2)-1)^(2)` are in A.P.

D

`S_(2), S_(12), S_(36)` are in G.P.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND SERIES

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|43 Videos

  • SOLUTION OF TRIANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|9 Videos

Similar Questions

Explore conceptually related problems

If S_(r) = sqrt(r+ sqrt(r+sqrt(r+sqrt(......oo)))) , r gt 0 then which the following is\are correct.

In triangle ABC, let b = 10, c = 10 sqrt(2) and R = 5 sqrt(2) then which of the following are correct

sum_(r =1)^(n) sin^(-1) ((sqrtr - sqrt(r -1))/(sqrtr(r + 1))) is equal to

Integrate the following w.r.t x sqrt(x)

Differentiate the following w.r.t x sqrt(sinx)

Integrate the following w.r.t x sqrt(1-sinx)

Consider int(x^(3)+3x^(2)+2x+1)/(sqrt(x^(2)+x+1))dx =(ax^(2)+bx+c)sqrt(x^(2)+x+1)+lambda int(dx)/(sqrt(x^(2)+x+1)) Now, match the following lists and then choose the correct code. Codes: {:(,a,b,c,d),((1),q,p,s,r),((2),s,p,q,r),((3),r,q,p,s),((4),q,s,p,r):}

If s = t + sqrt((r^(3))/(q)) , what is the value of r in terms of q, s and t ?

Differentiate sqrt(sin^(-1)sqrt(x)) w.r.t. x, ( 0 lt x lt 1 )

If r is positive real number such that 4sqrt(r)-(1)/(4sqrt(r))= 4, then find the value of 6sqrt(r)+(1)/(6sqrt(r)).

VK JAISWAL ENGLISH-SEQUENCE AND SERIES -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. It the first and (2n-1)^(th) terms of an A.P.,a G.P. and an H.P. of po...

    Text Solution

    |

  2. If a, b, c are distinct positive real numbers such that the quadratic ...

    Text Solution

    |

  3. If a,b,c are in H.P, where a gt c gt 0, then :

    Text Solution

    |

  4. In an A.P. let T(r) denote r ^(th) term from beginning, T(p) - (1)/(q ...

    Text Solution

    |

  5. Which of the following statement (s) is (are) correct ?

    Text Solution

    |

  6. If a,b,c are in 3 distinct numbers in H.P. a,b,c gt 0, then :

    Text Solution

    |

  7. All roots of equation x ^(5) -40 x ^(4) + alphax ^(3) + beta x ^(2) + ...

    Text Solution

    |

  8. Let a (1), a(2), a(3)……. be a sequence of non-zero rela numbers with a...

    Text Solution

    |

  9. Given a,b,c are in A.P. b,c,d are in G.P. and c,d,e are in H.P. if a =...

    Text Solution

    |

  10. The numbers a,b,c are in A.P. and a+b+c=60. The numbers (a-2), b, (c+3...

    Text Solution

    |

  11. If (x ^(2) +x+1) + (x^(2) + 2x +3) + (x^(2) + 3x +5) + ….. + (x ^(2) +...

    Text Solution

    |

  12. For Delta ABC, if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (whe...

    Text Solution

    |

  13. Let x,y,z in (0, (pi)/(2)) are first three consecutive terms of an ari...

    Text Solution

    |

  14. If the number 16, 20, 16, d form a A.G.P. then d can be equal to :

    Text Solution

    |

  15. Given then which of the following true

    Text Solution

    |

  16. If S(r) = sqrt(r+sqrt(r+sqrt(r+sqrt(r+.....oo)))),r gt 0, then which o...

    Text Solution

    |

  17. Consider the A.P. 50,48,46,44 ……. If S (n) denotes the sum to n terms ...

    Text Solution

    |

  18. Sum of the n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+(7)/(1^...

    Text Solution

    |

  19. For Delta ABC, if 81 + 144 a ^(4) + 16b ^(4) + 9c ^(4) =144 abc, (whe...

    Text Solution

    |