Home
Class 11
MATHS
If a1,a2,a3,.......an are in AP where a1...

If `a_1,a_2,a_3,.......a_n` are in AP where `a_1 gt 0foralli` then the value of `1/(sqrta_1+sqrta_2)+1/(sqrta_2+sqrta_3)+....1/(sqrta_(n-1)+sqrta_n=`

A

`1/(sqrta_1-sqrta_n`

B

`1/(sqrta_1-sqrta_n)`

C

`(n-1)/(sqrta_1+sqrta_n)`

D

`n/(sqrta_1-sqrta_n)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    PATHFINDER|Exercise QUESTION BANK|41 Videos

  • QUADRATIC EQUATION

    PATHFINDER|Exercise QUESTION BANK|19 Videos

Similar Questions

Explore conceptually related problems

Prove that lim_(x to 0) (sqrt(a+x)-sqrta)/x = 1/(2sqrta) ( a ne o)

If a_1+a_2+a_3+......+a_n=1 AA a_i > 0, i=1,2,3,......,n , then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n .

If a_1,a_2,.....a_n are in H.P., then the expression a_1a_2 + a_2a_3 + ... + a_(n-1)a_n is equal to

If a_1,a_2,.....a_n are positive real number whose product is a fixed number c, then the minimum value of a_1+a_2+......+a_(n-1)+a_n is

Three positive numbers a,b,c are in A.P prove that 1/(sqrtb+sqrtc) , 1/(sqrtc+sqrta) and 1/(sqrta+sqrtb) are aslo in A.P

If a_1 and a_2 are two non-collinear unit vectors and if |a_1+a_2|=sqrt(3) , then the value of (a_1-a_2)*(2a_1+a_2) is

If a_1,a_2,a3,...,a_n are in A.P then show 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 2x = sqrta+1/sqrta . Show that sqrt(x^2-1)/(x-sqrt(x^2-1))(a-1)

If a_1. a_2 ....... a_n are positive and (n - 1) s = a_1 + a_2 +.....+a_n then prove that (a_1 + a_2 +....+a_n)^n ge (n^2 - n)^n (s - a_1) (s - a_2)........(s - a_n)

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

    Text Solution

    |

  2. If the ratiio of the sum of n terms ofd two AP's is (3n+1):(2n+3) then...

    Text Solution

    |

  3. If a1,a2,a3,.......an are in AP where a1 gt 0foralli then the value of...

    Text Solution

    |

  4. Given p no. of A.P. each of which consists of an n terms. If their fir...

    Text Solution

    |

  5. Answer the following question based on above passage: The coefficient...

    Text Solution

    |

  6. If a,b,c ,d and p are distinct real number such that (a^2+b^2+c^2)p^2-...

    Text Solution

    |

  7. Suppose a,b,c are in A.P and a^2,b^2,c^2 are in G.P. If a lt b lt c an...

    Text Solution

    |

  8. The value of 4^(1/3).4^(1/9).4^(1/27)....infty is.

    Text Solution

    |

  9. If the sum of an infinite GP is 20 and sum of their square is 100 then...

    Text Solution

    |

  10. If S=1+a+a^2+....... t o infty , then a=

    Text Solution

    |

  11. If 4a^2+9b^2+16c^2=2(3ab+6bc+4ca) where a,b,c are non zero real number...

    Text Solution

    |

  12. If a,b,c in AP and x=sum(n=0)^inftya^n,y=sum(n-0)^inftyb^n,z=sum(n-0)^...

    Text Solution

    |

  13. If a,b,c are in G.P., then the equations ax^2+2bx+c =0 and dx^2+2ex+f ...

    Text Solution

    |

  14. If the product of n positive number is unity, then their sum is

    Text Solution

    |

  15. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |

  16. If a,b,c,d are positive real number such that a+b+c+d=2 , then M=(a+b)...

    Text Solution

    |

  17. If a1,a2,.....an are positive real number whose product is a fixed num...

    Text Solution

    |

  18. The greatest value x^2y^3 is, where xgt0 and ygt0 are connected by the...

    Text Solution

    |

  19. Let S=8/5+16/65+......128/(2^18+1) then

    Text Solution

    |

  20. The sum of the infinite terms of the series 5/(3^2. 7^2)+9/(7^2. 11^2)...

    Text Solution

    |