Home
Class 12
MATHS
If ar>0, r in N and a1.a2,....a(2n) are ...

If `a_r>0, r in N` and `a_1.a_2,....a_(2n)` are in A.P then `(a_1+a_2)/(sqrta_1+sqrta_2)+(a_2+a_(2n-1))/(sqrta_2+sqrta_3)+.....+(a_n+a_(n+1))/(sqrt a_n+sqrta_(n+1))=`

A

`n-1`

B

`(n(a_(1)+2_(2n)))/(sqrt(a_(1))+sqrt(a_(n+1)))`

C

`(n-1)/(sqrt(a_(1))+sqrt(a_(n+1)))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION & SERIES

    FIITJEE|Exercise EXERCISE 1|5 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise EXERCISE 2|4 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|11 Videos

  • PROBABILITY

    FIITJEE|Exercise Exercise 7|2 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If a_1,a_2,a_3….a_(2n+1) are in A.P then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to

If a_(1),a_(2),a_(3),"….",a_(n) are in AP, where a_(i)gt0 for all I, the value of (1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n)) is

If a_1,a_2,a_3,………a_n are in A.P, where a_igt0 for all i show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))+……..+1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,a_3,.....,a_n are in AP, prove that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+...+1/(a_(n-1)a_n)=(n-1)/(a_1a_n) .

If a_1,a_2,….a_n are in H.P then (a_1)/(a_2+,a_3,…,a_n),(a_2)/(a_1+a_3+….+a_n),…,(a_n)/(a_1+a_2+….+a_(n-1)) are in

FIITJEE-PROGRESSION & SERIES -SOLVED PROBLEMS (OBJECTIVE)
  1. The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2...

    Text Solution

    |

  2. If (a(2)a(3))/(a(1)a(4))=(a(2)+a(3))/(a(1)+a(4))=3((a(2)-a(3))/(a(1)-a...

    Text Solution

    |

  3. If ar>0, r in N and a1.a2,....a(2n) are in A.P then (a1+a2)/(sqrta1+sq...

    Text Solution

    |

  4. Find the greatest value of x^2y^3, w h e r exa n dy lie in the first q...

    Text Solution

    |

  5. Let p,q,repsilonR^(+) and 27pqr>=(p+q+r)^3 and 3p+4q+5r=12 then p^3+q^...

    Text Solution

    |

  6. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

    Text Solution

    |

  7. If three positive unequal numbers a, b, c are in H.P., then

    Text Solution

    |

  8. A geometric progression of real numbers is such that the sum of its ...

    Text Solution

    |

  9. If (a+bk)/(a-bk) = (b+ck)/(b-ck) = (c-dk)/(c-dk) where k != 0 , a, b ,...

    Text Solution

    |

  10. If three positive numbers a,b,c are in A.P ad tan^(-1)a,tan^(-1)b,tan^...

    Text Solution

    |

  11. Find the sum n terms of seires tan theta+1/2tantheta/2+1/(2^2)tantheta...

    Text Solution

    |

  12. sum (k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

    Text Solution

    |

  13. Find the sum of n terms the series: 1/(costheta+cos3theta0+1/(costheta...

    Text Solution

    |

  14. The 100^(th) term of the series 3+ 8+22+72+266+ 103+ ........is divisi...

    Text Solution

    |

  15. For the series 2+12+36+80+150+252 +….., the value of lim(n to oo) T/(n...

    Text Solution

    |

  16. Statement 1 : If a+2b+3c=1 and a gt 0 , b gt 0 , c gt 0 then the gre...

    Text Solution

    |

  17. For the series 21,22,23 ,…. K - 1 , k the A.M and G.M of the first ...

    Text Solution

    |

  18. A sequence a(1),a(2), …..a(n)of real numbers is such that a(1) = 0 ,|a...

    Text Solution

    |

  19. Let x(1),x(2),x(3)…..,x(n) be a sequence of integers such that -1 le x...

    Text Solution

    |

  20. If a = sum(r=1)^(oo) 1/(r^(2)), b = sum(r=1)^(oo) 1/((2r-1)^(2)), th...

    Text Solution

    |