Home
Class 11
MATHS
Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sq...

Sum of `1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/(sqrt(11)+sqrt(14))+..to n` terms= (A) `n/(sqrt(3n+2)-sqrt(2))` (B) `1/3 (sqrt(2)-sqrt(3n+2)` (C) `n/(sqrt(3n+2)+sqrt(2))` (D) none of these

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise All Questions|486 Videos

Similar Questions

Explore conceptually related problems

(2sqrt(-5)+3sqrt(-2))(-3sqrt(-8)-sqrt(-20))

Simplify: 1/sqrt(11-2sqrt(30))-3/(sqrt7-2sqrt(10))-4/(sqrt(8+4sqrt3))

Simplify: (sqrt2 (2 + sqrt3))/(sqrt3 (sqrt3 + 1)) - (sqrt2 (2 - sqrt3))/(sqrt3 (sqrt3 -1))

The sum of the numerical series 1/(sqrt3 + sqrt7) + 1/(sqrt7 + sqrt11) + 1/(sqrt11 + sqrt15) + ... upto n terms is

Simplify: (1)/(sqrt2 +1) + (1)/(sqrt3 + sqrt2) + (1)/(sqrt4 + sqrt3)

int (dx)/(sqrt(1+sqrt(x)))=(4)/(3)(sqrt(x)-2)sqrt(1+sqrt(x))+c

Show that (sqrt5 + sqrt3)/(sqrt5 - sqrt3) - (sqrt5 - sqrt3)/(sqrt5 + sqrt3) = 2 sqrt15

Let p=1+1/(sqrt(2))+1/(sqrt(3))+...+1/(sqrt(120)) and q=1/(sqrt(2))+1/(sqrt(3))+...+1/(sqrt(121)) then

Simplify: (3sqrt7)/(sqrt5 + sqrt2) - (5 sqrt5)/(sqrt2 + sqrt7) + (2 sqrt2)/(sqrt7 + sqrt5)

The sum of the series (1)/(sqrt1+sqrt2)+ (1)/(sqrt2+ sqrt3)+ ...+ (1)/(sqrt(n)+sqrt(n+1)) is equal to-

CENGAGE PUBLICATION-SEQUENCES AND SERIES-All Questions
  1. If tk is the kth term of a G.P., then show that t(n - k), tn, t(n + k)...

    Text Solution

    |

  2. If pth, qth, and rth term of an AP are equal to corresponding terms of...

    Text Solution

    |

  3. Sum of 1/(sqrt(2)+sqrt(5))+1/(sqrt(5)+sqrt(8))+1/(sqrt(8)+sqrt(11))+1/...

    Text Solution

    |

  4. If fourth term of an HP is 3/5 and its 8th term is 1/3 , then find it...

    Text Solution

    |

  5. If a,b, c are in GP, Prove that a^2, b^2 , c^2 are in GP.

    Text Solution

    |

  6. If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P....

    Text Solution

    |

  7. If (p^2+q^2), (pq+qr), (q^2+r^2) are in GP then Prove that p, q, r are...

    Text Solution

    |

  8. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

    Text Solution

    |

  9. Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5...

    Text Solution

    |

  10. Let the sum of first three terms of G.P. with real terms be 13/12 and ...

    Text Solution

    |

  11. 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=2 ...

    Text Solution

    |

  12. The terms a1,a2,a3 form an arithmetic sequence whose sum is 18.The ter...

    Text Solution

    |

  13. Let f(x)=2x+1. Then the number of real number of real values of x for ...

    Text Solution

    |

  14. Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The inte...

    Text Solution

    |

  15. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4 and t2+...

    Text Solution

    |

  16. If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G....

    Text Solution

    |

  17. If a,b,c,d are in GP then prove that, (a^2-b^2), (b^2-c^2), (c^2-d^2)...

    Text Solution

    |

  18. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

    Text Solution

    |

  19. If a, b, care in GP then prove that a^3, b^3, c^3 are in GP.

    Text Solution

    |

  20. The second term of an H.P. is 3/14 and the fifth term is 1/10 . Find...

    Text Solution

    |