Home
Class 11
MATHS
Give an example of a statement P(n) such...

Give an example of a statement P(n) such that P(3) is true, but P(4) is not true.

Text Solution

Verified by Experts

The correct Answer is:
`P(n):3n^(2) +n ` is divisible by 3 and so on
Promotional Banner

Topper's Solved these Questions

  • PRINCIPAL OF MATHEMATICAL INDUCTION

    CBSE COMPLEMENTARY MATERIAL|Exercise Very Short Answer Type Questions(M.C.Q)|3 Videos

  • PRACTICE PAPER-II

    CBSE COMPLEMENTARY MATERIAL|Exercise Section-D (Long Answer Type-I)|7 Videos

  • PROBABILITY

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS|23 Videos

Similar Questions

Explore conceptually related problems

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

Given an example of a statement P(n) which is true for all n>=4 but P(1),P(2) and P(3) are not true.Justify your answer.

Let P(n) denote the statement: 2^(n)ge n! .Show that P(1),P(2),P(3) are true butP(4) is not true.

If P(n) is the statement n^(3)+n is divisible by 3, prove that P(3) is true but P(4) is not true.

If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the statements P(3) and P(4) are true,but that P(5) is not true.

If P(n) is a statement (n in N) such that if P(k) is true,P(k+1) is true for k in N, then P(k) is true.

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

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

CBSE COMPLEMENTARY MATERIAL-PRINCIPAL OF MATHEMATICAL INDUCTION -Short Answer Type Questions
  1. Give an example of a statement P(n) such that P(3) is true, but P(4) i...

    Text Solution

    |

  2. If P(n) :1+4+7…….+(3n-2)=(1)/(2)n(3n-1).Verify P(n) for n =1,2.

    Text Solution

    |

  3. If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2)a n ...

    Text Solution

    |

  4. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  5. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  6. Prove the following by the principle of mathematical induction: a+(...

    Text Solution

    |

  7. Prove the following by the principle of mathematical induction: 7+7...

    Text Solution

    |

  8. sin x+sin 2x + sin 3x+...+ sin nx =(sin((n+1)/2)xsin(nx)/2)/sin(x/2)

    Text Solution

    |

  9. Using principle of mathematical induction prove that cosalpha\ cos2...

    Text Solution

    |

  10. Prove the following by the principle of mathematical induction: 1^2...

    Text Solution

    |

  11. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  12. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  13. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  14. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  15. 1 1^(n+2)+1 2^(2n+1) is divisible by 133.

    Text Solution

    |

  16. Using the principle of mathematical induction. Prove that (x^(n)-y^(n...

    Text Solution

    |

  17. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  18. 7^(2n) + 2^(3n-3).3^(n-1) is divisible by 25

    Text Solution

    |

  19. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |

  20. Prove the following by using the Principle of mathematical induction A...

    Text Solution

    |