Home
Class 11
MATHS
Let P(n) be the statement "3^n > n" . If...

Let `P(n)` be the statement `"3^n > n"` . If `P(n)` is true, `P(n+1)` is also true.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA ENGLISH|Exercise All Questions|182 Videos

Similar Questions

Explore conceptually related problems

Let P(n) be the statement: 2^n >= 3n . If P(r) is true, show that P (r + 1) is true. Do you conclude that P(n) is true for all n in N

If P(n) be the statement 2^ngtn^n and if P(m) is true, show tht P(m+1) is also true

Let P(n) be the statement ''(3)^(n)gt n'' . If P(n) is true , prove that P(n + 1) is true.

If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1) is true.

If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(r+1) is true.

The statement n! gt 2^(n-1), n in N is true for

If P (n) is the statement n^2> 100" , prove that whenever P(r) is true, P(r+1) is also true.

Let P(n) be the statement "7 divides 2^(3n)-1 ." What is P(n+1) ?

Let P(n) be a statement and let P(n) Rightarrow P(n+1) for all natural number n, then P(n) is true.

If P(n) is the statement "2^(3n)-1 . Is an integral multiple 7", and if P(r) is true, prove that P(r+1) is true.

RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. For all positive integer n , prove that (n^7)/7+(n^5)/5+2/3n^3-n/(105)...

    Text Solution

    |

  2. If P(n) is the statement "2^(3n)-1 . Is an integral multiple 7", and i...

    Text Solution

    |

  3. Let P(n) be the statement "3^n > n" . If P(n) is true, P(n+1) is also ...

    Text Solution

    |

  4. If P(n) is the statement n^2> 100" , prove that whenever P(r) is...

    Text Solution

    |

  5. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  6. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  7. Prove by the principle of mathematical induction that: n(n+1)(2n+1) is...

    Text Solution

    |

  8. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  9. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

    Text Solution

    |

  10. Prove that 1/(n+1)+1/(n+2)+...+1/(2n)> 13/24 ,for all natural number ...

    Text Solution

    |

  11. Prove the following by using the principle of mathematical inductio...

    Text Solution

    |

  12. Prove by induction the inequality (1+x)^ngeq 1+n x whenever x is pos...

    Text Solution

    |

  13. If P(n) is the statement n^3+n is divisible 3 is the statement P(3) tr...

    Text Solution

    |

  14. If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the...

    Text Solution

    |

  15. Let P(n) be the statement 7 divides (2^(3n)-1)dot What is P(n+1)?

    Text Solution

    |

  16. If P(n) is the statement n(n+1) is even, then what is P(3)?

    Text Solution

    |

  17. If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is t...

    Text Solution

    |

  18. If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1...

    Text Solution

    |

  19. If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(...

    Text Solution

    |

  20. Given an example of a statement P(n) such that it is true of all n ϵN.

    Text Solution

    |