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Does this work?(or did i do it wrong?)fp1 proof by induction Watch

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    \displaystyle\sum_{r=1}^n r(r+1) = \dfrac{n(n+1)(n+2)}{3}


    n=1
    \displaystyle\sum_{r=1}^1 r(r+1) = \dfrac{1(1+1)(1+2)}{3}


    2=2


    n=k
    \displaystyle\sum_{r=1}^k r(r+1) = \dfrac{k(k+1)(k+2)}{3}



    n=k+1
    \displaystyle\sum_{r=1}^{k+1} r(r+1) = \sum_{r=1}^{k+1} r(r+1) +[k+1(k+1+1)]



    \displaystyle\sum_{r=1}^{k+1} r(r+1) = \dfrac{k(k+1)(k+2)}{3}+[k+1(k+2)]



    \displaystyle\sum_{r=1}^{k+1} r(r+1) = \dfrac{k(k+1)(k+2)+3[(k+1)(k+2)]}{3}



    \displaystyle\sum_{r=1}^{k+1} r(r+1) = \dfrac{(k+3)(k+1)(k+2)}{3}



    \displaystyle\sum_{r=1}^{k+1} r(r+1) = \dfrac{k+1(k+1+1)(k+1+2)}{3}


    since true for n=1 it's therefore true for n=2,3,4.....


    also what does nez^+ mean? it's looks really cool but i don't understand it
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    Yes, it looks right, watch out for bracketing errors.

    This:

    n=k+1


    Should be this:

    

  \displaystyle\sum_{r=1}^{k+1} r(r+1) = \sum_{r=1}^{k} r(r+1) +( k+1)(k+1+1)

    But other than that it's all right.
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    (Original post by huiop)


    also what does nez^+ mean? it's looks really cool but i don't understand it
     n \in \mathbb Z_+ means " n is an element of the set of positive integers"
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    (Original post by huiop)
    Proof by induction...
    Good (though that 2=2 is pointless). Just be careful of the brackets; I'm sure you got them in there correctly on the paper.

    n\in \mathbb{Z_+} means n belongs to the set of positive integers. Another indication could be n\in \mathbb{N} where it means that n is in the subset of natural numbers, n\not=0
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    You must not write 2 = 2 that is not correct.

    Write LHS = 2 RHS = 2 so true for n = 1.
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    Your proof needs to have some explanation too - also see my comment above.
    For example,
    'Assume true for some n = k'
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    (Original post by NotNotBatman)
    Yes, it looks right, watch out for bracketing errors.

    This:

    n=k+1


    Should be this:

    

  \displaystyle\sum_{r=1}^{k+1} r(r+1) = \sum_{r=1}^{k} r(r+1) +( k+1)(k+1+1)

    But other than that it's all right.
    oops, yes i was trying to correct them all before the replies came
    (Original post by NotNotBatman)
     n \in \mathbb Z_+ means " n is an element of the set of positive integers"
    ???? i don't quite understand
    (Original post by RDKGames)
    Good (though that 2=2 is pointless). Just be careful of the brackets; I'm sure you got them in there correctly on the paper.

    n\in \mathbb{Z_+} means n belongs to the set of positive integers. Another indication could be n\in \mathbb{N} where it means that n is in the subset of natural numbers, n\not=0
    oops yea... corrected now...

    so is it suppsoed to mean n is any positive number? i don't quite understand i know n by itself just means n, the e stands for any then the z i don't know what that is :/
    (Original post by Muttley79)
    You must not write 2 = 2 that is not correct.

    Write LHS = 2 RHS = 2 so true for n = 1.
    o.o
    ok so that's a better way to express it?
    (Original post by Muttley79)
    Your proof needs to have some explanation too - also see my comment above.
    For example,
    'Assume true for some n = k'
    ok thanks
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    (Original post by huiop)
    oops yea... corrected now...

    so is it suppsoed to mean n is any positive number? i don't quite understand i know n by itself just means n, the e stands for any then the z i don't know what that is :/
    Top line of: http://www.math.ku.edu/~porter/Math_symbols%20.pdf

    By saying n \in \mathbb{Z} you are restricting what types of values n can be. The Z gets rid off any fractions and irrationals, thus leaving positive/negative integers. By saying n \in \mathbb{Z_+} you are specifying it further down to only POSITIVE integers.
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    (Original post by RDKGames)
    Top line of: http://www.math.ku.edu/~porter/Math_symbols%20.pdf

    By saying n \in \mathbb{Z} you are restricting what types of values n can be. The Z gets rid off any fractions and irrationals, thus leaving positive/negative integers. By saying n \in \mathbb{Z_+} you are specifying it further down to only POSITIVE integers.
    ooh ok so it means any positive integer thanks a ton
 
 
 
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