Home
Class 11
MATHS
Prove the following by using the princip...

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

Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    PSEB|Exercise EXERCISE|53 Videos

  • PROBABILITY

    PSEB|Exercise EXERCISE|95 Videos

Similar Questions

Explore conceptually related problems

Prove the following by using the principle of mathematical induction for all n in N :- (2n+7) < (n + 3)^2.

Prove the following by using the principle of mathematical induction for all n in N :- a + ar + ar^2+...+ ar^(n-1)=(a(r^n-1))/(r-1) .

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 2.3^2 + 3.3^3 +... + n.3^n =((2n-1)3^(n+1) +3)/4 .

Prove the following by using the principle of mathematical induction for all n in N :- 1 +2 + 3 +...+n < 1/8(2n+1)^2 .

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

Prove the following by using the principle of mathematical induction for all n in N :- 1.2 + 2.3 + 3.4 +... +n.(n+1)=[(n(n+1)(n+2))/3]

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

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 3.5 + 5.7 +...+ (2n-1)(2n+1)=(n(4n^2 +6n-1))/3

Prove the following by using the principle of mathematical induction for all n in N :- 1.2.3 + 2.3.4 +...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 .

Prove the following by using the principle of mathematical induction for all n in N :- 1/2+1/4+1/8+...+1/2^n=1-1/2^n .

PSEB-PRINCIPLE OF MATHEMATICAL INDUCTION-EXERCISE
  1. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

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

    Text Solution

    |

  3. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  18. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  19. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |

  20. Prove the following by using the principle of mathematical induction f...

    Text Solution

    |