Home
Class 11
MATHS
Given an example of a statement P(n) suc...

Given an example of a statement `P(n)` such that it is true of all `n inNdot`

Text Solution

Verified by Experts

`P(n) = 1 + 2 + 3 + - - - - - + n = (n(n+1))/2`
` P(n)` is true for all natural numbers
. Hence, `P(n)` is true for all `n∈N`
Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos
  • MATHEMATICAL REASONING

    RD SHARMA|Exercise Solved Examples And Exercises|181 Videos

Similar Questions

Explore conceptually related problems

Give an example of a statement P(n) such that P(3) is true, but P(4) is not true.

Given an example of a statement P(n) which is true for all n>=4 but P(1),P(2) and P(3) are not true.Justify your answer.

Choose the statement which is correct for all n in N

Let P(n) be a statement such that P(n) Rightarrow P(n+1) for all n in NN . Also, if P(k) is true, k in N , then we can conclude that.-

The statement n! gt 2^(n-1), n in N is true for

Let P(n) be the statement : n^(2) +n is even Is P(n) true for all ninN ?

Let P(n) be the statement : ”n^(2)+n is even" Prove that P(n) is true for all n in N by Mathematical Induction

If P(n) is a statement (n in N) such that if P(k) is true,P(k+1) is true for k in N, then P(k) is true.

Which statement is true about n/p ratio?

RD SHARMA-MATHEMATICAL INDUCTION-Solved Examples And Exercises
  1. If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1...

    Text Solution

    |

  2. If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(...

    Text Solution

    |

  3. Given an example of a statement P(n) such that it is true of all n inN...

    Text Solution

    |

  4. If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2) and...

    Text Solution

    |

  5. Given an example of a statement P(n) which is true for all ngeq4 but P...

    Text Solution

    |

  6. Prove by the principle of mathematical induction that for all n N ...

    Text Solution

    |

  7. Using principle of mathematical induction prove that x^(2n)-y^(2n) i...

    Text Solution

    |

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

    Text Solution

    |

  9. Prove by induction that 4+8+12++4n=2n(n+1) for all n Ndot

    Text Solution

    |

  10. Using principle of mathematical induction prove that cosalpha\ cos2a...

    Text Solution

    |

  11. Let U1=1,\ U2=1\ a n d\ U(n+2)=U(n+1)+Unfor\ ngeq1. use mathematical i...

    Text Solution

    |

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

    Text Solution

    |

  13. Prove the following by the principle of mathematical induction: 1^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Prove the following by the principle of mathematical induction:1/(2...

    Text Solution

    |

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

    |