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    How does equal this? -- when finfding the sum of the series

    \displaystyle\sum_{r=1}^n 3^r = \frac{3}{2}(3^n-1)

    I understand stand it when it just r or r sqaured, cubed etc.., but what do you do when it's to the power of r? Whats the standard result?
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    Write out a few terms.

    This should be a series you recognise...
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    (Original post by emmaxoxo)
    How does equal this? -- when finfding the sum of the series

    \displaystyle\sum_{r=1}^n 3^r = \frac{3}{2}(3^n-1)

    I understand stand it when it just r or r sqaured, cubed etc.., but what do you do when it's to the power of r? Whats the standard result?
    Is this chapter 5 or chapter 6 - proof by induction?
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    (Original post by emmaxoxo)
    How does equal this? -- when finfding the sum of the series

    \displaystyle\sum_{r=1}^n 3^r = \frac{3}{2}(3^n-1)

    I understand stand it when it just r or r sqaured, cubed etc.., but what do you do when it's to the power of r? Whats the standard result?
    The standard result is:
    \displaystyle\sum_{r=1}^n a^r = \frac{n}{n-1}(a^n-1)
    A similar result that might be useful is:
    \displaystyle\sum_{r=0}^n a^r = \frac{1}{n-1}(a^{n+1}-1)
    I'm pretty sure you could prove these with induction if you needed to.
 
 
 
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