Home
Class 12
MATHS
If a1+a2+a3+...+an=1AAai>0,i=1,2,3, ,n ,...

If `a_1+a_2+a_3+...+a_n=1AAa_i>0,i=1,2,3, ,n ,` then find the maximum value of `a_1 a_2a_3a_4a_5.... a_n.`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.1|8 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise 6.2|6 Videos

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Comprehension|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

Similar Questions

Explore conceptually related problems

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 (1+x-2x^2)^(20)=a_0+a_1x+a_2x^2+a_3x^3+...+a_(40)x^(40), then find the value of a_1+a_3+a_5+...+a_(39)dot

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.....

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n

Let a1,a2,a3 ...... a11 be real numbers satisfying a_1 =15, 27-2a_2 > 0 and a_k= 2a_(k-1) - a_(k-2) for k=3,4,.....11 If (a1^2 +a2^2.......a11^2)/11 = 90 then find the value of (a_1+a_2....+a_11)/11

If (1+x-2x^2)^6=1+a_1 x+a_2 x^2+a_2 x^3+......... , then the value of a_2+a_4+a_6+......+a_12 will be

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If roots of an equation x^n-1=0 are 1,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 (a) n (b) n^2 (c) n^n (d) 0

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)

If a_1,a_2, .....,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 a. a_(n-1)+2a_n b. (n+1)c^(1//n) c. 2n c^(1//n) d. (n)(2c)^(1//n)

CENGAGE-INEQUALITIES INVOLVING MEANS -Examples
  1. Prove that 2^n >1+nsqrt(2^(n-1)),AAn >2 where n is a positive integer.

    Text Solution

    |

  2. If S+a1+a2+a3++an ,a1 in R^+ for i=1ton , then prove that S/(S-a1)+S/...

    Text Solution

    |

  3. If a1+a2+a3+...+an=1AAai>0,i=1,2,3, ,n , then find the maximum value o...

    Text Solution

    |

  4. If a , b , c , are positive real numbers, then prove that (2004, 4M) {...

    Text Solution

    |

  5. Prove that (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha)ge8. If ea...

    Text Solution

    |

  6. Prove that [(x^2+y^2+z^2)/(x+y+z)]^(x+y+z)gtx^xy^yz^zgt[(x+y+z)/(3)]...

    Text Solution

    |

  7. Prove that 1^(2)+2^(2)+3^(2)+.....+n^(2)=(n(n+1)(2n+1))/6

    Text Solution

    |

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

    Text Solution

    |

  9. Find the maximum value of (7-x)^4(2+x)^5w h e nx lies between -2a n d7...

    Text Solution

    |

  10. Find the maximum value of xyz when (x)/(1)+(y^2)/(4)+(z^3)/(27)=1, whe...

    Text Solution

    |

  11. If a,bgt0 such that a^3+b^3=2 , then show that a+ble 2.

    Text Solution

    |

  12. If m >1,n in N show that 1m+2m+2^(2m)+2^(3m)++2^(n m-m)> n^(i-m)(2^n-...

    Text Solution

    |

  13. Prove that n in acute angled triangle ABC , sec A+sec B +sec Cge 6.

    Text Solution

    |

  14. Prove that (b^2+c^2)/(b+c)+(c^2+a^2)/(c+a)+(a^2+b^2)/(a+b)gt a+b+c , w...

    Text Solution

    |

  15. Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

    Text Solution

    |

  16. If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)2+(b+1//c)...

    Text Solution

    |

  17. Let x1, x2, ,xn be positive real numbers and we define S=x1+x2++xndot...

    Text Solution

    |

  18. If 2x^3 +ax^2+ bx+ 4=0 (a and b are positive real numbers) has 3 real ...

    Text Solution

    |

  19. Calculate the greatest and least values of the function f(x)=(x^4)/(x...

    Text Solution

    |

  20. If a,b,c are three distinct positive real numbers in G.P., than prove ...

    Text Solution

    |