Sum of a Series

[ChaoticLlama]

I don't know what method I should use to evaulate this infinite series.

What is the value of \(\displaystyle \L\sum\limits_{n = 1}^\infty {\frac{{2^{n + 1} }}{{3^n }}}\)

With basic algebra that series is equal to: \(\displaystyle \L\ 2\sum\limits_{n = 1}^\infty {\left( {\frac{2}{3}} \right)} ^n\)

Any help would be appreciated.

 

[ChaoticLlama]

Wait a second, I think I just stumbled upon the answer.

Do I not treat this as a standard geometric series? where...

\(\displaystyle \L\ S_\infty = \frac{1}{{1 - \frac{3}{4}}} = 4\)

 

[Gene]

A winning plan!
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Gene