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Math Help - ~~~inequality-- hard

  1. #1
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    MATHEMATICAL INDUCTION~~~inequality-- hard

    hey guys!! can anyone help me with this hard question?
    its to do with mathematical induction (inequalitites)
    i think im missing a step in my proof and i just cant figure it out....

    heres the question:

    Prove that 2^n>3n for all positive integers where n is greater than or equal to 4

    thanks guys
    any help would be great
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  2. #2
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    Quote Originally Posted by fring
    hey guys!! can anyone help me with this hard question?
    its to do with mathematical induction (inequalitites)
    i think im missing a step in my proof and i just cant figure it out....
    heres the question:
    Prove that 2^n>3n for all positive integers where n is greater than or equal to 4

    thanks guys
    any help would be great
    Hello, fring,

    I presume, that you know, that this proof has to be done in 3 steps:

    1. 2^4 > 3*4 is true

    2. ***ume that 2^n > 3*n for all n greater than 4

    3. Proof (under ***umption step 2) that
    2^{n+1}>3(n+1)
    2^n*2>3n+3
    2^n+2^n>3n+3

    Compare both sides of this inequality: 2^n >3n according to ***umtion (step 2). Because 2^n > 3 for all n greater than 4 the last inequality is true for all n.

    Greetings

    EB

    PS: The writing with 3 stars was not done by me. Someone in this forum had set a filter to avoid all disgusting words. Kind of funny!
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