Home
Class 11
MATHS
Prove, by Induction, on the inequality (...

Prove, by Induction, on the inequality `(1 +x)^n ge 1 +nx`
for all natural numbers n, where x > - 1.

Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise EXERCISE|85 Videos

  • LINEAR INEQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE|289 Videos

  • MATHEMATICAL MODELLING

    MODERN PUBLICATION|Exercise EXAMPLE|3 Videos

Similar Questions

Explore conceptually related problems

Show that ^nP_n= "^nP_(n-1) for all natural numbers n .

If A = [(1,1),(1,1)] , prove by induction that A^n = [(2^(n-1), 2^(n-1)), (2^(n-1), 2^(n-1))] for all natural numbers n.

Prove using mathematical induction:- n(n+1)(n+5) is divisible by 6 for all natural numbers

Prove that : (2n) ! = 2^n (n!)[1.3.5.... (2n-1)] for all natural numbers n.

By Mathematical Induction, prove that : (1+1/n)^n len for all nge3 .

Prove that log_n(n+1)>log_(n+1)(n+2) for any natural number n > 1.

Use the principle of mathematical induction to show that 5^(2n+1)+3^(n+2).2^(n-1) divisible by 19 for all natural numbers n.

Prove by Principle of Mathematical Induction, that (n^5/5 + n^3/3+ (7n)/15) is a natural number for all n in N.

Show by using the principle of mathematical induction that for all natural number n gt 2, 2^(n) gt 2n+1

MODERN PUBLICATION-MATHEMATICAL INDUCTION-EXERCISE
  1. Use method of induction, prove that : n(n +1)(n +2) is divisible by 6.

    Text Solution

    |

  2. Use method of induction, prove that : n^3+3n^2+5n+3 is divisible by 3...

    Text Solution

    |

  3. Prove, by Induction, on the inequality (1 +x)^n ge 1 +nx for all natu...

    Text Solution

    |

  4. Let P(n) be the statement "n^2-n+41" is prime. Prove that P(1), P(2) a...

    Text Solution

    |

  5. Let P(n) be the statement : “the arithmetic mean of n and (n + 2) is t...

    Text Solution

    |

  6. If n straight lines in a plane are such that no two of them are parall...

    Text Solution

    |

  7. Let P (n) denote the statement : “2^n gen !". Show that P(1), P(2) an...

    Text Solution

    |

  8. By using the Principle of Mathematical Induction, prove the following ...

    Text Solution

    |

  9. By using the Principle of Mathematical Induction, prove the following ...

    Text Solution

    |

  10. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  11. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  12. By using the Principle of Mathematical Induction, prove the following ...

    Text Solution

    |

  13. By using the Principle of Mathematical Induction, prove the following...

    Text Solution

    |

  14. By using the Principle of Mathematical Induction, prove the following ...

    Text Solution

    |

  15. Prove, by Mathematical Induction, that for all n in N, 3^(2n)-1 is d...

    Text Solution

    |

  16. 10^n+3(4^(n+2))+5 is divisible by (n in N)

    Text Solution

    |

  17. Prove, by Mathematical Induction, that for all n in N, 2.7^n+3.5^n-5...

    Text Solution

    |

  18. Prove, by Mathematical Induction, that for all n in N, n(n + 1) (n +...

    Text Solution

    |

  19. By Mathematical Induction, prove the following : (4^n+ 15n -1) is di...

    Text Solution

    |

  20. By Mathematical Induction, prove the following : 12^n +25^(n-1) is d...

    Text Solution

    |