Home
Class 11
MATHS
Prove that 2^n gt n for all positive int...

Prove that `2^n gt n` for all positive integtrs n.

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    V PUBLICATION|Exercise QUESTIONBANK|79 Videos

  • PROBABILITY

    V PUBLICATION|Exercise QUESTION BANK|89 Videos

Similar Questions

Explore conceptually related problems

Using mathematical induction prove that d/(d x)(x^n)=n x^(n-1) for all positive integers n .

If a_1=1 and a_n= na_(n-1) for all positive integer n ge 2 then a_5 is equal to

Prove that (1 + sqrt3i)^n + (1 - sqrt3i)^n = 2^(n+1) cos ((npi)/3) for any positive integer n

Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1) Hence by using the principle of mathematical induction, prove that P(n) is true for all natural numbers n .

Prove that (1+x)^n ge1+n x , for all natural number 'n', where x gt-1 .

If A and B are square matrices of the same order such that A B=B A ,then prove by induction that AB^n=B^n A . Further, prove that (AB)^n = A^n B^n for all n in N .

If a and b are distinct integers prove that a-b is a factor of a^n-b^n whenever n is a positive integer.

Prove that the function f(x)=x^n is continuous at x=n, where n is a positive integer.

Consider the statement P(n):1/1.2+1/2.3+1/3.4+.....+1/{n(n+1)}=n/(n+1) .Prove that P(n) is true for all n in N using the principle of mathematical induction.

Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in N

V PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. For all n gt 1 , prove that 1^(2)+2^(2)+3^(2)+4^(2)+...........+n^(2) ...

    Text Solution

    |

  2. Prove that 2^n gt n for all positive integtrs n.

    Text Solution

    |

  3. For all nge1, prove that 1/1.2+1/2.3+1/3.4+..........+1/(n(n+1))=n/(...

    Text Solution

    |

  4. For every positive integer n,prove that 7^n-3^n is divisible by 4 usin...

    Text Solution

    |

  5. Prove that (1+x)^n ge1+n x, for all natural number 'n', where x gt-1.

    Text Solution

    |

  6. For all nge1, prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

    Text Solution

    |

  7. For all nge1, prove that 1^2+2^2+3^2+……….+n^2gtn^3/3

    Text Solution

    |

  8. Prove that the rule of exponents (a b)^n=a^n b^n by using principle of...

    Text Solution

    |

  9. Prove by using the principal of Mathematical Induction P(n)=1+3+3^2+…....

    Text Solution

    |

  10. Using mathematical induction prove that 1^3+2^3+3^3+.....+n^3=[(n(n+1)...

    Text Solution

    |

  11. For all nge1, prove that 1+1/((1+2))+1/((1+2+3))+.......+1/((1+2+3+....

    Text Solution

    |

  12. For all nge1, prove that 1.2.3+2.3.4+......+n(n+1)(n+2)=(n(n+1)(n+2)(n...

    Text Solution

    |

  13. Using mathematical induction prove 1cdot3+2cdot3^2+3cdot3^3+.....+ncdo...

    Text Solution

    |

  14. Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the prin...

    Text Solution

    |

  15. Using mathematical induction prove that 1cdot3+3cdot5+5cdot7+.....+(...

    Text Solution

    |

  16. Using mathematical induction prove that 1cdot2+2cdot2^2+......+ncdot...

    Text Solution

    |

  17. A statement p(n) for a natural number n is given by p(n):1/2+1/4+1/8...

    Text Solution

    |

  18. Using mathimatical induction prove that 1/(2.5)+1/(5.8)+1/(8.11)+......

    Text Solution

    |

  19. Using mathematical induction prove that 1/(1.2.3)+1/(2.3.4)+......+1...

    Text Solution

    |

  20. Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-...

    Text Solution

    |