Home
Class 11
MATHS
State First principle of mathematical in...

State First principle of mathematical induction.

Text Solution

Verified by Experts


The first principle of mathematical induction states that if the basis step and the inductive step are proven, then P(n) is true for all natural numbers.
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

Prove the following by using the principle of mathematical induction. n(n+1)+1 is an odd natural number, n in N .

Second principal of mathematical induction

If A=[111011001] ,then use the principle of mathematical induction to show that A^(n)=[1nn(n+1)/201n001] for every positive integer n.

Prove by the principle of mathematical induction that n<2^(n) for alln in N

Prove by the principle of mathematical induction that for all n in N,3^(2n) when divided by 8, the remainder is always 1.

Use the principle of mathematical induction to show that a^(n) - b^9n) is divisble by a-b for all natural numbers n.

Prove by the principle of mathematical induction that for all !=psi lonN;n^(2)+n is even natural no.

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

Prove the following by using the principle of mathematical induction for all n in Nvdotsn(n+1)(n+5) is a multiple of 3.

RD SHARMA-MATHEMATICAL INDUCTION-Solved Examples And Exercises
  1. Prove the following by the principle of mathematical induction: (n^...

    Text Solution

    |

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

    Text Solution

    |

  3. Prove the following by the principle of mathematical induction: 1/2t...

    Text Solution

    |

  4. Prove the following by the principle of mathematical induction: (1-...

    Text Solution

    |

  5. Prove the following by the principle of mathematical induction: ((2...

    Text Solution

    |

  6. Prove the following by the principle of mathematical induction: \ x^...

    Text Solution

    |

  7. Prove that: \ sin x+sin3x++sin(2n-1)x=(sin^2\ \ n x)/(sin x) for all n...

    Text Solution

    |

  8. Given a1=1/2(a0+A/(a0)), a2=1/2(a1+A/(a1)) and a(n+1)=1/2(an+A/(an)) ...

    Text Solution

    |

  9. Let P(n) be the statement: 2^n >= 3n. If P(r) is true, show that P (r...

    Text Solution

    |

  10. The distributive law from algebra states that for all real numbers c,a...

    Text Solution

    |

  11. State First principle of mathematical induction.

    Text Solution

    |

  12. Write the set of values of n for which the statement P(n):2n < n! is t...

    Text Solution

    |

  13. State Second principal of mathematical induction.

    Text Solution

    |

  14. If P(n):2xx4^(2n+1)+3^(3n+1) is divisible by lambda for all n in N is ...

    Text Solution

    |

  15. If x^n-1 is divisible by x-lambda, then the least prositive integral v...

    Text Solution

    |

  16. For all n in N , 3xx5^(2n+1)+2^(3n+1) is divisible by a.19 b. 17 c. 23...

    Text Solution

    |

  17. If 10^n+3xx4^(n+2)+lambda is divisible by 9 or all natural numbers, t...

    Text Solution

    |

  18. Let P(n):2^n<(1xx2xx3xxxxn) . Then the smallest positive integer for w...

    Text Solution

    |

  19. A student was asked to prove a statement by induction. He proved (i) P...

    Text Solution

    |

  20. If P(n): 49^n+16^n+lambda is divisible by 64 for n in N is true, then ...

    Text Solution

    |