Home
Class 11
MATHS
If a1,a2,.....an are positive real numbe...

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

A

`n(c)^(1/n)`

B

`(n+1)c^(1/n)`

C

`2nc^(1/n)`

D

`(n+1)(2c)^(1/n)`

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 a_(1),a_(2),a_(3),a_(4),...,a_(n) are n 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 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)

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

Let vec r_1, vec r_2, vec r_3, .....vec r_n be the position vectors of points P_1,P_2, P_3 ,......P_n relative to the origin O . If the vector equation a_1 vec r_1+a_2 vec r_2+.....a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a) a_1+a_2+......a_n=n b) a_1+a_2+....a_n=1 c) a_1+a_2+....a_n=0 d) a_1=a_2=a_3+a_n=0

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)

Find the number of all three elements subsets of the set {a_1, a_2, a_3, ........... a_n} which contain a_3dot

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

PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
  1. If x1gt0,i=1,2.....50 and x1+x2+.....x50=50 then the minimum value of ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. The sum to infinity of the series 1+2/3+6/3^2+10/3^3+14/3^4+....

    Text Solution

    |

  8. The sum to n terms of the series 1+2(1+1/n)+3(1+1/n)^2+....... is give...

    Text Solution

    |

  9. For absx lt1 the value of 1+3x+6x^2+10x^3+.....t o infty is

    Text Solution

    |

  10. If pth, qth, and rth term of an AP are equal to corresponding terms of...

    Text Solution

    |

  11. If a,b,c are positive real number, then the least value of (a+b+c)(1/a...

    Text Solution

    |

  12. An infinite GP has first term x and sum 5, then x belongs to

    Text Solution

    |

  13. 2^(1/4),2^(2/8),2^(3/16),2^(4/32)......infty is equal to

    Text Solution

    |

  14. Let alpha , beta be the roots of x^2-x+p=0 and gamma,delta be the root...

    Text Solution

    |

  15. If f(x) is a function satisfying f(x+y)=f(x)f(y) for all x,yin N such ...

    Text Solution

    |

  16. Sum of n terms of the series 8+88+888+....equals

    Text Solution

    |

  17. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

    Text Solution

    |

  18. The sum of integer in between 1 to 100 which is divisible by 2 or 5 is

    Text Solution

    |

  19. 1/2+3/4+7/8+15/16+..... t o n terms =

    Text Solution

    |

  20. 0ltthetaltpi/2, if x=sum(n=0)^inftycos^(2n)theta,y=sum(n=0)^inftysin^(...

    Text Solution

    |