Home
Class 11
MATHS
By the principle of mathematical inducti...

By the principle of mathematical induction prove that the following statement are true for all natural numbers 'n' ` n (n+1) (n+5)` is a multiple of 3.

Text Solution

Verified by Experts

N/a
Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4.1|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 4.1|1 Videos

  • PERMUTATION AND COMBINATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|11 Videos

  • PROBABILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|10 Videos

Similar Questions

Explore conceptually related problems

By the principle of mathematical induction prove that the following statements are true for all natural numbers 'n' (a) (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+......+(1)/((2n-1)(2n+1)) =(n)/(2n+1) (b) (1)/(1.4)+(1)/(4.7)+(1)/(7.10)+......+(1)/((3n-2)(3n+1)) =(n)/(3n+1)

Using the principle of mathematical induction, prove that n<2^n for all n in N

Prove by the principle of mathematical induction that 2^ n >n for all n∈N.

Prove by the principle of mathematical induction that n<2^n"for all"n in Ndot

Use the principle of mathematical induction to show that a^(n) - b^n) is divisble by a-b for all natural numbers n.

By the principle of mathematical induction prove that for every n in N, the following statements are true: 1 +5 +9 + ....+ (4n - 3) = 2n^2 - n

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Using the principle of mathematical induction prove that 41^n-14^n is a multiple of 27 .

Using the principle of mathematical induction, prove that n(n+1)(n+5) is a multiple of 3 for all ninN .

NAGEEN PRAKASHAN ENGLISH-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise 4
  1. By the principle of mathematical induction prove that for all natural ...

    Text Solution

    |

  2. By the principle of mathematical induction prove that the following st...

    Text Solution

    |

  3. By the principle of mathematical induction prove that the following s...

    Text Solution

    |

  4. Prove the following by the principle of mathematical induction:\ 2....

    Text Solution

    |

  5. Prove by induction that the sum Sn=n^3+3n^2+5n+3 is divisible by 3 for...

    Text Solution

    |

  6. " if " a^(1) =a,a^(r+1) =a^(r).a " prove that :" (ab)^(n) =a^(n)b^(n...

    Text Solution

    |

  7. By the principle of mathematical induction prove that 3^(2^(n))-1, is ...

    Text Solution

    |

  8. Prove the following by the principle of mathematical induction:\ 7^...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Using the principle of mathematical induction ,prove that (1+x)^ngeq(1...

    Text Solution

    |

  12. Using binomial theorem, prove that 2^(3n)-7n-1 is divisible by 49 , wh...

    Text Solution

    |

  13. 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+n)=(2n)/(n+1)

    Text Solution

    |

  14. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

    Text Solution

    |

  15. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

    Text Solution

    |

  16. 1.3+2.3^2+3.3^3+..............+n.3^n=((2n-1)3^(n+1)+3)/4

    Text Solution

    |

  17. Prove by PMI that 1.2+ 2.3+3.4+....+ n(n+1) =((n)(n+1)(n+2))/3, AA n i...

    Text Solution

    |

  18. 1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^2+6n-1))/3

    Text Solution

    |

  19. Prove the following by the principle of mathematical induction: \ 1...

    Text Solution

    |

  20. Prove the following by the principle of mathematical induction:1/2+...

    Text Solution

    |