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`.

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

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

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 .

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

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=

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)

Let a_1, a_2, a_3.......... be in A.P. and h_1,h_2,h_3..... ,in H.P. If a_1=2 = h_1, and a_30=25=h_30 then a_7h_24+ a_14 + a_17=

Let a_1,a_2,a_3,.......a_11 be real number satisfying a_1=15,27-2a_2gt0 anda_k=2a_(k-1)-a_(k-2) for k=3,4,.....11. If (a_1^2+a_2^2+......a_11^2)/11=90, then the value of (a_1 +a_2+.....a_11)/11 is equal to

S.D. of numbers observation a_1, a_2, a_3,…..a_n is sigma then the S.D. of the observations lambdaa_1, lambdaa_2, lambdaa_3, lambdaa_3,....... lambdaa_n is

If roots of an equation x^n-1=0a r e1,a_1,a_2,..... a_(n-1), then the value of (1-a_1)(1-a_2)(1-a_3)(1-a_(n-1)) will be n b. n^2 c. n^n d. 0

CENGAGE PUBLICATION-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 log2(a+b)+log2(c+d)ge4 . Then the minimum value of the expression a...

    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. If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

    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 number whose product is a fixed num...

    Text Solution

    |

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

    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 triangle A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq...

    Text Solution

    |

  18. Prove that in A B C ,tanA+tanCgeq3sqrt(3,) where A , B , C are circle...

    Text Solution

    |

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

    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

    |