Home
Class 11
MATHS
Let P(n) : n(n+1)(n+2) is divisible by 6...

Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statement is true or false, when n=3 and n=5. Justify your answer.

Text Solution

Verified by Experts

True, True
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|209 Videos

  • PROBABILITY

    A N EXCEL PUBLICATION|Exercise QUESTION BANK|215 Videos

Similar Questions

Explore conceptually related problems

Determine whether the statement is true or false. Justify your answer. tan((5pi)/4)=1rArrtan^-1 1=(5pi)/4

(a) P(n):n(n+1)(n+2) is divisible by 6,then find P(3) .

Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true for all natural numbers? Justify your answer.

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify the statement for n=2.

Given P(n):3^(2n) -1 is divisible by 8 Check whether P(1) is true.

Let P(n) denotes the statement 2^(n+3) le (n+3)! Are P(1) and P(2) true? Justify your answer.

Given P(n):3^(2n) -1 is divisible by 8. If P(k) is true then prove P(k+1) is true.

(b) P(n):7^n-3^n is divisible by 4,then find P(2) .

Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Verify the statement for n=1.

Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the statement p(1) true? justify your answer

A N EXCEL PUBLICATION-PRINCIPLE OF MATHEMATICL INDUCTION-QUESTION BANK
  1. Using mathematical induction prove that x^(2n)-y^(2n) is divisible by ...

    Text Solution

    |

  2. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove ...

    Text Solution

    |

  3. Using mathematical induction prove that 41^n-14^n is a multiple of 2...

    Text Solution

    |

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

    Text Solution

    |

  5. Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the state...

    Text Solution

    |

  6. Consider the statement P(n):2^(3n) -1 is divisible by 7 If p(k) is t...

    Text Solution

    |

  7. Let P(n) be the statement "n+3" is prime. Is P(3) true? What is your...

    Text Solution

    |

  8. Let P(n) denotes the statement 10^(2n-1)+1 is divisible by 11. If P(m)...

    Text Solution

    |

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

    Text Solution

    |

  10. Let P(n) : n(n+1)(n+2) is divisible by 6. Determine whether the statem...

    Text Solution

    |

  11. Let P(n) denotes the statement 2^n gt n and if P(n) is true, show that...

    Text Solution

    |

  12. Show that x^n-1 is divisible by x-1

    Text Solution

    |

  13. Let P(n) denotes the statement '3^n gt 2^n'. Is P(1) true?

    Text Solution

    |

  14. By using mathematical induction prove that 1+4+7+...+(3n-2)=(n(3n-1))/...

    Text Solution

    |

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

    Text Solution

    |

  16. For all nge1, prove that 1/1.3+1/3.5+1/5.7+......+1/((2n-1)(2n+1))=n...

    Text Solution

    |

  17. Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 ...

    Text Solution

    |

  18. Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 ...

    Text Solution

    |

  19. Let P(n) denotes the statement 2^(n+3) le (n+3)! Are P(1) and P(2) tru...

    Text Solution

    |

  20. By mathematical induction prove that the statement 3^(4n+1)+2^(2n+2) i...

    Text Solution

    |