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Slow morning. Can someone help me figure it out? I have a feeling it is trivially easy and not worthy of a thread. $$ 3^{n+1} + 3^n = 4\cdot3^n $$

Thanks.

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    Did you mean $4\times 3^n$? I.e. $3^n$ instead of $3n$.2012-04-22
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    Yes. Edited. . .2012-04-22
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    When I have a very slow morning, I use [wolfram alpha](http://www.wolframalpha.com/input/?i=Solve[3^%28n%2B1%29%2B3n%3D%3D4*3^n]) ;-)2012-04-22

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Answers this version of the question

The previous version of the question claimed that for all $n \in \Bbb N$, $$3^{n+1}+3n=4\cdot 3n \tag{1}$$

However $(1)$ is not true for all $n$ as noted in the next part of the answer.

However what is true is: $$3^{n+1}+3^n=4\cdot3^n$$

To see this, note that $3^{n+1}=3^n \cdot 3$ and factor the $3^n$ out.

Answers the previous version of the question

Your claim is simply not true. For $n=2$, LHS equals $ 33$ while RHS evaluates to $24$.

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    Christ. I am stupid. Thanks2012-04-22
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    No you are not. But this feeling can make you one. So, please do not think this way, Regards,2012-04-22
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Hint: Write $3^{n+1}$ as $3\cdot 3^n$, then factor $3^n$ out of the sum.

(I assume the question is about $3^{n+1}+3^n$.)