Home
Class 11
MATHS
For all nge1, prove that p(n):n(n+1)(n+5...

For all `nge1`, prove that `p(n):n(n+1)(n+5)` is divisible by 3.

Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATIONS

    MAXIMUM PUBLICATION|Exercise EXAMPLE|171 Videos

  • PROBABILITY

    MAXIMUM PUBLICATION|Exercise EXAMPLE|98 Videos

Similar Questions

Explore conceptually related problems

For all nge1 , prove that p(n):n^3+(n+1)^3+(n+2)^3 is divisible by 9.

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

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.

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

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

(a)Prove that 3^(2n)-1 is divisible by 8.

Using binomial thẹorem, prove that 3^(3 n)-26 n-1 is divisible by 676 , where n in N

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

Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assume that P(k) is true for a natural number k, Verify that P(k+1) is true.

By mathematical induction prove that the statement 3^(4n+1)+2^(2n+2) is divisible by 7 is true for all n in N

MAXIMUM PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-EXAMPLE
  1. For all nge1, prove that 1.2.3+2.3.4+......+n(n+1)(n+2)=(n(n+1)(n+2)(n...

    Text Solution

    |

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

    Text Solution

    |

  3. For all nge1, prove that p(n):n(n+1)(n+5) is divisible by 3.

    Text Solution

    |

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

    Text Solution

    |

  5. Consider the statement ''p(n):9^n-1 is a multiple of 8''. Where n is a...

    Text Solution

    |

  6. Consider the statement ''p(n):9^n-1 is a multiple of 8''. Where n is a...

    Text Solution

    |

  7. Consider the statement ''P(n):x^n-y^n is divisible by x-y''. Show th...

    Text Solution

    |

  8. Consider the statement ''P(n):x^n-y^n is divisible by x-y''. Using t...

    Text Solution

    |

  9. Consider the statement ''7^n-3^n is divisible by 4'' Verify the resu...

    Text Solution

    |

  10. Consider the statement ''7^n-3^n is divisible by 4'' Prove the state...

    Text Solution

    |

  11. Which among the following is the least number that will divide 7^(2n)-...

    Text Solution

    |

  12. Prove by mathematical induction. (costheta +i sintheta)^n=(cosntheta...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true f...

    Text Solution

    |

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

    Text Solution

    |

  17. By the Principal of mathematical induction, prove that 1+5+5^2+…..+5^(...

    Text Solution

    |

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

    Text Solution

    |

  19. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assum...

    Text Solution

    |

  20. Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 C...

    Text Solution

    |