Home
Class 11
MATHS
Find the positive integer n for which th...

Find the positive integer n for which the inequality `2^(n)gtn^(2)` is true.

Text Solution

Verified by Experts

The correct Answer is:
`n=1` and `ngt4`
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

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

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

The number of positive integers satisfying the inequality .^(n+1)C_(n-2) - .^(n + 1)C_(n - 1) le 100 is

If n >1 , the value of the positive integer m for which n^m+1 divides a=1+n+n^2+ddot+n^(63) is/are a. 8 b. 16 c. 32 d. 64

Find the least positive integer n such that ((2i)/(1+i))^n is a positive integer.

Let a >2 be a constant. If there are just 18 positive integers satisfying the inequality (x-a)(x-2a)(x-a^2)<0, then find the value of adot

Let a >2 be a constant. If there are just 18 positive integers satisfying the inequality (x-a)(x-2a)(x-a^2)<0, then the value of a is ____________

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

If n is a positive integer then .^(n)P_(n) =

If n be a positive integer, then the digit in the unit's place of 3^(2n-1)+2^(2n-1) is -

CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Exercise
  1. If ninNN, then by principle of mathematical induction prove that, 3^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Prove by induction method that n(n^(2)-1) is divisible by 24 when n is...

    Text Solution

    |

  16. Find the positive integer n for which the inequality 2^(n)gtn^(2) is ...

    Text Solution

    |

  17. Prove by the method of mathematica induction that for all ninNN,3^(2n)...

    Text Solution

    |

  18. Prove by induction that 5^(n+1)+4*6^(n) when divided by 20 leaves the ...

    Text Solution

    |

  19. Prove by induction that 2^(2^(n))+1 has 7 in unit's place for all nge2...

    Text Solution

    |

  20. Using mathematical induction prove that for every integer n,|sinnx|le ...

    Text Solution

    |