Home
Class 11
MATHS
If angt1 for all ninN,then log(a2)a1+log...

If `a_ngt1` for all `ninN`,then `log_(a_2)a_1+log_(a3)a_2+.....+log_(an)a_(n-1)+log_(a1)a_n` has the minimum value

A

N

B

2

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
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

If n >1 ,then prove that 1/((log)_2n)+1/((log)_3n)+.......+1/((log)_(53)n)=1/((log)_(53 !)n)dot

If a_1,a_2,a_3,.....a_n.... are in G.P. then the determinant Delta=|[log a_n, log a_(n+1), log a_(n+2)],[log a_(n+3),loga_(n+4),log a_(n+5)],[log a_(n+6),log a_(n+7),log a_(n+8)]| is equal to- (A) -2 (B) 1 (C) -1 (D) 0

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> 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 the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

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)

Express M in terms of N: 1/2 log_(3) M +log_(3)N=1

If a_1,a_2…,a_n are in G.P. then evalute.: |{:(loga_n,loga_(n+1),loga_(n+2)),(loga_(n+3),loga_(n+4),loga_(n+5)),(loga_(n+6),loga_(n+7),loga_(n+8)):}|=0

If S=a_1+a_2+......+a_n,a_i in R^+ for i=1 to n, then prove that S/(S-a_1)+S/(S-a_2)+......+S/(S-a_n) ge n^2/(n-1), AA n ge 2

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. The solution of the equation (8)^((1+[cosx absdivcos^2xabsdiv cos^3x]d...

    Text Solution

    |

  2. If (1+x)(1+x^2)(1+x^4)....(1+x^128)=sum(r=0)^nx^r then n is

    Text Solution

    |

  3. If angt1 for all ninN,then log(a2)a1+log(a3)a2+.....+log(an)a(n-1)+log...

    Text Solution

    |

  4. Let Sk=underset(nrarrinfty)limsum(i=0)^n1/(k+1)^i. Then sum(k=1)^nkSk...

    Text Solution

    |

  5. If a1,a2,a3...an are in HP and f(k)=sum(r=1)^nar-ak, then a1/(f(1)),a...

    Text Solution

    |

  6. sum(r=1)^nr^2-sum(m=1)^nsum(r=1)^mr is equal to

    Text Solution

    |

  7. The sum of the integer from 1 to 100 which is not divisible by 3 or 5 ...

    Text Solution

    |

  8. If ab^2c^3,a^2b^3c^4,a^3b^4c^5 are in AP (a,b,cgt0) thgen the minimum...

    Text Solution

    |

  9. If the sum of n terms of the series 1/1^3+(1+2)/(1^3+2^3)+(1+2+3)/(1^3...

    Text Solution

    |

  10. The coefficient of x^(n-2) in the polynomial (x-1)(x-2)(x-3)....(x-n) ...

    Text Solution

    |

  11. The series of natural number is divided into groups as follows , (1), ...

    Text Solution

    |

  12. The sum of 10 terms of the series (x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^3)...

    Text Solution

    |

  13. If the sequence 1,2,2,4,4,4,4,,8,8,8,8,8,8,8,8,.... where n consecutiv...

    Text Solution

    |

  14. Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+.... is

    Text Solution

    |

  15. The cubes of the natural numbers are grouped as 1^3,(2^3,3^3),(4^3,5^3...

    Text Solution

    |

  16. Let f(n)=[1/2+n/100] where [x] denote the integral part of x. Then th...

    Text Solution

    |

  17. ABC is a right angled triangle in which angleB=90^@ and BC=a. If n poi...

    Text Solution

    |

  18. If a,b,c are three distinct positive real number such that a^2+b^2+c^2...

    Text Solution

    |

  19. The sum of the series 1^3 - 2^3 + 3^3 - ....+ 9^3=

    Text Solution

    |

  20. If x1, x2 , x3 and y1 , y2 , y3 are both in G.P. with the same common ...

    Text Solution

    |