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November 16th, 2014, 05:44 PM   #1
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Series Exponent

Hello,

I am starting with series and I have an example from the book but I cannot figure out what they did with the exponents.

Can anyone help?

I want to know how to go from the first expression to the second one.

$\displaystyle \sum_{n=1}^{\infty}\frac{4^{n}}{3^{n-1}}=\sum_{n=1}^{\infty}4(\frac{4}{3})^{n-1}$

Thanks
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November 16th, 2014, 06:06 PM   #2
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Hello Admins,

I am so sorry. I posted this here. I was looking for the LaTex and I posted without noticing I was in the incorrect section.

Can you move it?

Thanks
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November 16th, 2014, 06:24 PM   #3
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$$4^n = 4 \times 4^{n-1}$$so$$\frac{4^n}{3^{n-1}} = 4\times \frac{4^{n-1}}{3^{n-1}} = 4 \left( \frac43 \right)^{n-1}$$
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November 16th, 2014, 06:32 PM   #4
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Quote:
Originally Posted by v8archie View Post
$$4^n = 4 \times 4^{n-1}$$so$$\frac{4^n}{3^{n-1}} = 4\times \frac{4^{n-1}}{3^{n-1}} = 4 \left( \frac43 \right)^{n-1}$$
Thanks a lot. So simple lol This series and sequences are killing me
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January 9th, 2015, 08:36 PM   #5
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Have you tried graphing it yet?
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