Home
Class 11
MATHS
Prove the following by the principle of ...

Prove the following by the principle of mathematical induction: `1/(1. 4)+1/(4. 7)+1/(7. 10)+....+1/((3n-2)(3n+1))=n/(3n+1)`

Text Solution

Verified by Experts

Let P (n) be the given statement.
i.e., `P (n) : 1/(1.4) + 1/(4.7) + 1/(7.10) + .... + 1/[(3n - 2)(3n + 1)] = n/(3n + 1)`
For `n = 1,`
...
Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT ENGLISH|Exercise EXERCISE 4.1|24 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT ENGLISH|Exercise EXERCISE 7.1|6 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise All Questions|71 Videos

Similar Questions

Explore conceptually related problems

Prove the following by the principle of mathematical induction: 1/(3. 7)+1/(7. 11)+1/(11. 15)+.....+1/((4n-1)(4n+3))=n/(3(4n+3))

Prove the following by the principle of mathematical induction: 1/(2. 5)+1/(5. 8)+1/(8. 11)++1/((3n-1)(3n+2))=n/(6n+4)

Prove the following by the principle of mathematical induction: 1/(3. 5)+1/(5. 7)+1/(7. 9)+1/((2n+1)(2n+3))=n/(3(2n+3))

Prove the following by the principle of mathematical induction: 1/(1. 2)+1/(2. 3)+1/(3. 4)++1/(n(n+1))=n/(n+1)

Prove the following by the principle of mathematical induction: 1/2+1/4+1/8++1/(2^n)=1-1/(2^n)

Prove the following by the principle of mathematical induction: 1+3+3^2++3^(n-1)=(3^n-1)/2

Prove the following by the principle of mathematical induction: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by using the principle of mathematical induction for all n in N : 1/(3. 5)+1/(5. 7)+1/(7. 9)+...+1/((2n+1)(2n+3))=n/(3(2n+3)) .

Prove the following by using the principle of mathematical induction for all n in N : 1/(2. 5)+1/(5. 8)+1/(8. 11)+...+1/((3n-1)(3n+2))=n/((6n+4))

Prove the following by the principle of mathematical induction: \ 1^2+3^2+5^2++(2n-1)^2=1/3n(4n^2-1)

NCERT ENGLISH-PRINCIPLE OF MATHEMATICAL INDUCTION-EXERCISE 4.1
  1. Prove the following by using the principle of mathematical induction ...

    Text Solution

    |

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

    Text Solution

    |

  3. Prove the following by the principle of mathematical induction: 1/(1...

    Text Solution

    |

  4. Prove by the principal of mathematcal induction that for all n in N. ...

    Text Solution

    |

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

    Text Solution

    |

  6. Prove the following by the principle of mathematical induction:\ n(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Prove by the principle of induction that for all n N ,\ (10^(2n-1)+1)...

    Text Solution

    |

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

    Text Solution

    |

  13. Prove the following by the principle of mathematical induction: 1+3...

    Text Solution

    |

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

    Text Solution

    |

  15. Using the principle of mathematical induction, prove that 1+1/(1+2)+...

    Text Solution

    |

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

    Text Solution

    |

  17. Using the principle of mathematical induction prove that : 1. 3+2. 3^...

    Text Solution

    |

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

    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...

    Text Solution

    |