Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By JeffM

Thread: discrete maths

  1. #1
    Banned
    Joined
    Nov 2016
    From
    Hounshigh
    Posts
    3

    discrete maths

    I will let D be a function that contains elements n from the set of Natural Numbers: N


    i define D(n) = 2 x 3^c
    .... .. .................. c=0



    (b) Prove this sentance by induction:
    for all n which are elements from set Natural Numbers: N, D(n) = 3^(n+1) +1


    Base case: when n is 1 D(1) = 3^(1+1) + 1 = 9 + 1 = 10

    Inductive step: we assume that D(n) = 3^(n+1) is true for n = k, hence D(k) = 3^(k+1) + 1 is true
    We prove that D(k) = 3^(k+1) + 1



    sorry for my english i am from italy. this is what im quite unsure about what is happen here and if im doing it right, how do i prove now?
    Last edited by PussyEnjoyer; Nov 20th 2016 at 10:49 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Feb 2014
    From
    United States
    Posts
    1,703
    Thanks
    802

    Re: discrete maths

    I am very confused.

    $\displaystyle GIVEN:\ n \in \mathbb N^+\ and\ D(n) = 2 * \sum_{c=0}^n3^c.$

    $PROVE: D(n) = 3^{(n+1)} + 1.$

    Is that correct?

    $D(1) = 2(3^0 + 3^1) = 2(1 + 3) = 8 \ne 10 = 9 + 1 = 3^{(1+1)} + 1.$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Nov 2016
    From
    Hounshigh
    Posts
    3

    Re: discrete maths

    Quote Originally Posted by JeffM View Post
    I am very confused.

    $\displaystyle GIVEN:\ n \in \mathbb N^+\ and\ D(n) = 2 * \sum_{c=0}^n3^c.$

    $PROVE: D(n) = 3^{(n+1)} + 1.$

    Is that correct?

    $D(1) = 2(3^0 + 3^1) = 2(1 + 3) = 8 \ne 10 = 9 + 1 = 3^{(1+1)} + 1.$
    Oh my bad that is all correct except the statement that we have to prove by induction the end bit is -1 not +1.

    So yeah all of its correct and i have to prove the sentance by induction:
    Prove by induction: D(n)=3^(n+1)-1.

    EDIT: The working out i done at top is that not correct because proof by induction it say you need base case and induction step.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Nov 2016
    From
    Hounshigh
    Posts
    3

    Re: discrete maths

    Can someone tell me how i prove it by induction please?
    Last edited by PussyEnjoyer; Nov 20th 2016 at 12:42 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    15,770
    Thanks
    3496

    Re: discrete maths

    Show true for $D(1)$ ... you can do this.

    Assume true for $D(n)$, show true for $D(n+1)$

    $\displaystyle D(n)=2\sum_{c=0}^n 3^c = 3^{n+1}-1$

    $\displaystyle D(n+1) = 2\sum_{c=0}^{n+1} 3^c = 2\sum_{c=0}^n 3^c + (2 \cdot 3^{n+1}) = 3^{n+1}-1 + 2\cdot 3^{n+1}=$

    $3 \cdot 3^{n+1}-1 = 3^{n+2}-1 =3^{(n+1)+1}-1$


    in future, do not bump your thread ... thank you for cooperating.
    Last edited by skeeter; Nov 20th 2016 at 02:07 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Feb 2014
    From
    United States
    Posts
    1,703
    Thanks
    802

    Re: discrete maths

    Quote Originally Posted by PussyEnjoyer View Post
    hey bro thanks. That final answer 3^((n+1)+1) - 1, is that correct?
    Yes, that is correct.

    You sent me a private message about formatting. It may help others if I answer publicly.

    This site supports a formatting system called LaTeX. Most of the regular tutors use it, and you can see how it works by hitting reply with quote instead of reply. Unless you are going to post regularly, I suggest that you concentrate on math rather than LaTeX because the latter is a fussy beast. If you are going to post frequently, you may as well learn it because your questions will be easier to understand. There is a forum here that will answer specific questions about LaTeX, and there are good teaching resources on the Internet.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Discrete Maths
    Posted in the Discrete Math Forum
    Replies: 9
    Last Post: Jan 18th 2010, 06:58 AM
  2. discrete maths
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Nov 21st 2009, 07:44 AM
  3. discrete maths
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Jun 19th 2009, 10:23 PM
  4. Discrete maths
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Mar 2nd 2009, 10:50 AM
  5. discrete maths
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Feb 27th 2009, 07:22 AM

/mathhelpforum @mathhelpforum