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

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

Text Solution

Verified by Experts

Given,`1+3+3^2+.......+3^(n−1)=(3^(n)−1)/2​`
Let P(n)=`1+3+3^2+.......+3^(n−1)=(3^(n)−1)/2​`
when n=1
P(1)=1
SO,P(n) is true 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: 2+5+8+11++(3n-1)=1/2n\ (3n+1)

Prove the following by the principle of mathematical induction: \ 7^(2n)+2^(3n-3). 3^(n-1) is divisible 25 for all n in Ndot

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

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

Prove the following by the principle of mathematical induction: 1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

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

Prove the following by the principle of mathematical induction: (1-1/(2^2))(1-1/(3^2))(1-1/(4^2))------(1-1/(n^2))=(n+1)/(2n) for all natural numbers \ ngeq2.

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

Prove the following by the principle of mathematical induction: \ x^(2n-1)+y^(2n-1) is divisible by x+y for all n in NNdot

Prove the following by the principle of mathematical induction: 1+2+3++n=(n(n+1))/2idote , the sum o the first n natural numbers is (n(n+1))/2dot

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 the principle of mathematical induction: 1/(1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    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:1/2+...

    Text Solution

    |