Home
Class 11
MATHS
For what natural numbers n the inequalit...

For what natural numbers n the inequality `2^(n)gt2n+1` is valid ?

Text Solution

Verified by Experts

The correct Answer is:
`nge3`
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|12 Videos

  • STRAIGHT LINE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion-Reason Type)|2 Videos

Similar Questions

Explore conceptually related problems

For which natural numbers n the inequality 2^ngt2n+1 is true?

The value of the natural numbers n such that the inequality 2^ngt2n+1 is valid is :

The natural number n for which the inequality 2 ^(n) gt 2n+1 is valid, is-

For every natural number n, show that 7^(2n)+2^(3n-3)*3^(n-1) is always divisible by 25.

Median of 1st n natural numbers is

For every natural number n(gt1) , show that , 4^(n)+15n-1 is divisible by 9 .

If n is a natural number then (12 ^(n) + 25 ^(n-1)) is divisible by-

If n is a natural number, then (4^(n) -3n -1) is always divisible by-

A function f from the set of natural numbers N to the set of integers Z is defined by f(n)={((n-1)/(2),"when n is odd"),(-(n)/(2),"when n is even"):} Then f(n) is -

If p be a natural number, then prove that, p^(n+1)+(p+1)^(2n-1) is divisible by (p^(2)+p+1) for every positive integer n.

CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Exercise
  1. For all ninNN, prove by principle of mathematical induction that, 15...

    Text Solution

    |

  2. For all ninNN, prove by principle of mathematical induction that, 12...

    Text Solution

    |

  3. For what natural numbers n the inequality 2^(n)gt2n+1 is valid ?

    Text Solution

    |

  4. 3^(2n+2)-8n-9 is divisible by

    Text Solution

    |

  5. If ninNN, then by principle of mathematical induction prove that, 10...

    Text Solution

    |

  6. If ninNN, then by principle of mathematical induction prove that, 3^...

    Text Solution

    |

  7. If ninNN, then by principle of mathematical induction prove that, 3^...

    Text Solution

    |

  8. If ninNN, then by principle of mathematical induction prove that, 7+...

    Text Solution

    |

  9. If ninNN, then by principle of mathematical induction prove that, 1+...

    Text Solution

    |

  10. If ninNN, then by principle of mathematical induction prove that, 1^...

    Text Solution

    |

  11. If ninNN, then by princuple of mathematical induction prove that, (1...

    Text Solution

    |

  12. If ninNN, then by princuple of mathematical induction prove that, (n...

    Text Solution

    |

  13. If ninNN, then by princuple of mathematical induction prove that, n*...

    Text Solution

    |

  14. If ninNN, then by principle of mathematical induction prove that, Pr...

    Text Solution

    |

  15. If ninNN, then by principle of mathematical induction prove that, Us...

    Text Solution

    |

  16. If ninNN, then by princuple of mathematical induction prove that, 2+...

    Text Solution

    |

  17. If ninNN, then by principle of mathematical induction prove that, .^...

    Text Solution

    |

  18. If x and are two real numbers, then prove by mathematical induction th...

    Text Solution

    |

  19. By induction method prove that, (a^(n)+b^(n)) is divisible by (a+b) wh...

    Text Solution

    |

  20. If ninNN and (2*1+1)+(2*2+1)+(2*3+1)+ . . .+(2*n+1)=n^(2)+2n+5 is tr...

    Text Solution

    |