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msingh

principle of mathematical induction

  • one year ago
  • one year ago

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  1. msingh
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    just one thing wanna ask why we take n=1

    • one year ago
  2. msingh
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    and n=k+1

    • one year ago
  3. Mertsj
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    The simplest and most common form of mathematical induction proves that a statement involving a natural number n holds for all values of n. The proof consists of two steps: The basis (base case): showing that the statement holds when n is equal to the lowest value that n is given in the question. Usually, n = 0 or n = 1. The inductive step: showing that, with respect to each n for which the statement holds, then the statement must also hold when n + 1 is substituted for n.

    • one year ago
  4. msingh
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    but we can't take n=0

    • one year ago
  5. Mertsj
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    So you show it is true for one value. Then show it is true for 1 more than that value. That shows it is true for all.

    • one year ago
  6. Mertsj
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    Not if you're using natural numbers only. Then you might want to take n = 1

    • one year ago
  7. msingh
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    k

    • one year ago
  8. Mertsj
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    Notice it says take the lowest value that n (k if you prefer) is given in the question.

    • one year ago
  9. Mertsj
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    Show it is true for k. Then the inductive step...show it is true for k+1

    • one year ago
  10. Mertsj
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    http://www.youtube.com/watch?v=QHkG0d5kZvE

    • one year ago
  11. Mertsj
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    Maybe that video will help.

    • one year ago
  12. msingh
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    k

    • one year ago
  13. DLS
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    @msingh You should be polite while conversing with other people on OS and try to make some efforts for giving a proper reply followed by a thanks if a user helped you. It hardly takes your time to write "Okay" rather than k. Just an advice :]

    • one year ago
  14. DLS
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    Because I see @Mertsj is making a great effort to help you.

    • one year ago
  15. msingh
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    okay..i will keep in mind

    • one year ago
  16. msingh
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    @Mertsj thank u sis

    • one year ago
  17. Mertsj
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    I know you are thankful, msingh. You always say so and you are most welcome.

    • one year ago
  18. Mertsj
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    I only hope that was helpful.

    • one year ago
  19. msingh
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    yes,,it was helpful for me

    • one year ago
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