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Math Help - Mathematical Induction

  1. #1
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    Mathematical Induction

    Hi guys, im new to the forum and was wandering if you guys could help me with a question on mathematical induction, its part of an assignment I have to complete and its been bugging me for a while, thanks in advance if you could help me out!

    The question is an image i will upload.
    Mathematical Induction-induction-question.jpg

    May i add i have tried and it has worked for the base case.
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  2. #2
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    Write as \displaystyle\frac{1}<br />
{{\left( {3i - 1} \right)\left( {3i + 2} \right)}} = \frac{1}<br />
{{3\left( {3i - 1} \right)}} - \frac{1}<br />
{{3\left( {3i + 2} \right)}}.
    Last edited by Plato; August 31st 2010 at 03:11 PM.
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  3. #3
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    sorry for asking but what difference does it make if the lhs is changed? i thought the main focus was the rhs
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  4. #4
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    Quote Originally Posted by zirly View Post
    sorry for asking but what difference does it make if the lhs is changed? i thought the main focus was the rhs
    Well for one it turns the sums into collapsing sums.
     \displaystyle <br />
\sum\limits_{i = 1}^3 {\frac{1}<br />
{{\left( {3i - 1} \right)\left( {3i + 2} \right)}}}  = \sum\limits_{}^{} {\left[ {\frac{1}<br />
{{3\left( {3i - 1} \right)}} - \frac{1}<br />
{{3\left( {3i + 2} \right)}}} \right]}
     \displaystyle = \left( {\frac{1}<br />
{6} - \frac{1}<br />
{{15}}} \right) + \left( {\frac{1}<br />
{{15}} - \frac{1}<br />
{{24}}} \right) + \left( {\frac{1}<br />
{{24}} - \frac{1}<br />
{{33}}} \right) = \left( {\frac{1}<br />
{6} - \frac{1}<br />
{{33}}} \right)
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