Home
Class 11
MATHS
Prove that [(n+1)//2]^n >(n !)dot...

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

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

Prove that ((n + 1)/(2))^(n) gt n!

If U_n=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n) , then prove that U_(n+1)=8U_n-4U_(n-1)dot

Prove that: n !(n+2)=n !+(n+1)!

Prove that ((2n+1)!)/(n !)=2^n{1. 3. 5 .........(2n-1)(2n+1)}

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

Prove that 2 le (1+ (1)/(n))^(n) lt 3 for all n in N .

If I_n=int_0^(pi//4)tan^("n")x dx , prove that I_n+I_(n-2)=1/(n-1)dot

If S_1 be the sum of (2n+1) term of an A.P. and S_2 be the sum of its odd terms then prove that S_1: S_2=(2n+1):(n+1)dot

Prove that (.^n C_0)/1+(.^n C_2)/3+(.^n C_4)/5+(.^n C_6)/7+ . . . =(2^n)/(n+1)dot

If I_n=int_0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_n

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. In a triangle A B C prove that a//(a+c)+b//(c+a)+c//(a+b)<2

    Text Solution

    |

  2. Find the least value of secA+secB+secC in an acute angled triangle.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. 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

    |

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

    Text Solution

    |