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Math Help - Induction question help needed

  1. #1
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    Induction question help needed

    Prove by induction that

    (1 +x)**n ≥ 1 + nx

    i have never seen a induction question set up like this before ... could i get some assistance please

    im confused as to how to use both n and x in the question
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  2. #2
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    Re: Induction question help needed

    You are using a notation that is not standard for many mathematicians. This was already mentioned in response to one of your previous posts. Standard notation to indicate an exponent is ^, not **. Your posts will be easier for the general community to read if you try to learn LaTeX (and use [tex][/tex] or $\$\$$ tags) or use notation that is more familiar to most mathematicians.

    For your question, I assume that x can be any real number, and n is a positive integer. Start with the base of induction:

    (1+x)^1 = 1+x = 1+1x

    Note: if n=0, then it is still true for all x\neq -1, as (1+x)^0=1=1+0x for all x\neq -1.

    Assume it is true for all positive integers up to some value n. Then try to show that (1+x)^{n+1} \ge 1+(n+1)x. Hint: (1+x)^{n+1} = (1+x)(1+x)^n.
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  3. #3
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    Re: Induction question help needed

    yeah i realize that i a problem ill research how to do that ... thanks for the help ill look at it and try to continue
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