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Math Help - Need help with mathematical induction.

  1. #1
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    Need help with mathematical induction.

    Here's a problem from tonight's homework that I am stuck on.

     3+8+13+18+...+(5n-2)=\frac{n}{2}(5n+1)

    Here's the work I did up to the point I'm stuck:

    s_{1}=3=\frac{1}{2}[5(1)+1]\surd
    s_{k}=3+8+13+18+...+(5n-2)=\frac{k}{2}(5k+1)
    s_{k+1}=3+8+13+18+...+(5n-2)+[5(k+1)-2]
    =s_{k}+(5k+3)
    =\frac{k}{2}(5k+1)(5k+3)

    I know that s_{k+1} is supposed to equal \frac{k+1}{2}(5k+6) when it's all said and done. But at this point, I cannot figure out how to reach that.

    I will greatly appreciate any and all help.
    Last edited by mathgeek777; April 24th 2008 at 10:58 AM. Reason: Editing signs
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by mathgeek777 View Post
     3+8+13+18+...+(5n-2)=\frac{n}{2}(5n{\color{red}+}1)
    It should be easier to work with that.
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  3. #3
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    The minus sign was put in incorrectly. But I still came out to the right conclusion on the work I gave.

    Still need help folks
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Let's evaluate s_{k+1} : s_{k+1}=s_k+(5k+3)=\frac{k}{2}(5k+1)+(5k+3)=\frac{  5k^2+k+10k+6}{2}=\frac{5k^2+11k+6}{2} hence \boxed{s_{k+1}=\frac{(k+1)(5k+6)}{2}}<br />
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  5. #5
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    Of course it looks so obvious .

    Thank you sir for the assistance. It is appreciated greatly.
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