Home
Class 11
MATHS
If a1+a2+a3+......+an=1 AA ai > 0, i=1,...

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`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+....+a_(n-1)+3a_n is

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+.......a_(n-1)+2a_n is

If for an A.P. a_1,a_2,a_3,........,a_n,........a_1+a_3+a_5=-12 and a_1a_2a_3=8, then the value of a_2+a_4+a_6 equals

If A_1,A_2,A_3, A_4 and A_5 are the five A.M.'s between 2 nd 8, then find the value of A_1+A_2+A_3+A_4+A_5

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_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .

If a_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .

Consider an A. P .a_1,a_2,a_3,..... such that a_3+a_5+a_8 =11and a_4+a_2=-2 then the value of a_1+a_6+a_7 is.....

Consider an A.P. a_1, a_2, a_3,......... such that a_3+a_5+a_8=11 and a_4+a_2=-2, then the value of a_1+a_6+a_7 is (a). -8 (b). 5 (c). 7 (d). 9

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Find the least value of secA+secB+secC in an acute angled triangle.

    Text Solution

    |

  2. Prove that [(n+1)//2]^n >(n !)dot

    Text Solution

    |

  3. If a1+a2+a3+......+an=1 AA ai > 0, i=1,2,3,......,n, then find the ma...

    Text Solution

    |

  4. If a ,b ,c are positive, then prove that a//(b+c)+b//(c+a)+c//(a+b)geq...

    Text Solution

    |

  5. If (log)(10)(x^3+y^3)-(log)(10)(x^2+y^2-x y)lt=2, and x ,y are positiv...

    Text Solution

    |

  6. If (log)2(a+b)+(log)2(c+d)geq4. Then find the minimum value of the exp...

    Text Solution

    |

  7. If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

    Text Solution

    |

  8. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

    Text Solution

    |

  9. Prove that b^2c^2+c^2a^2+a^2b^2> a b cxx(a+b+c)(a ,b ,c >0) .

    Text Solution

    |

  10. Find the minimum value of 4sin^(2)x+4cos^(2)x .

    Text Solution

    |

  11. Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

    Text Solution

    |

  12. The minimum value of the sum of real number a^-5,a^-4,3a^-3,1,a^8 and ...

    Text Solution

    |

  13. If a1,a2,------ ,an are positive real numbers whose product is a fixe...

    Text Solution

    |

  14. If a ,b ,c ,d are positive real umbers such that a+b+c+d=2,then M=(a+...

    Text Solution

    |

  15. A straight line through the vertex P of a triangle P Q R intersects th...

    Text Solution

    |

  16. If alpha in (0,pi/2), then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is alw...

    Text Solution

    |

  17. In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

    Text Solution

    |

  18. In Delta A B C , prove that t a n A+t a n B+t a n Cgeq3sqrt(3),w h e...

    Text Solution

    |

  19. If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+...

    Text Solution

    |

  20. If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

    Text Solution

    |