(adsbygoogle = window.adsbygoogle || []).push({}); Some sums, don't sum up :)

I have a problem that require some math tricks, and after I tried to solve it myself I looked at the answer and I don't understand how this is done :

[tex]

\[

\sum\limits_{k = 0}^n {\left( {\frac{2}{5}} \right)^k } + \sum\limits_{k = 0}^n {\left( {\frac{3}{5}} \right)^k } = \frac{5}{3}\left( {1 - \left( {\frac{2}{5}} \right)^{n + 1} } \right) + \frac{5}{2}\left( {1 - \left( {\frac{3}{5}} \right)^{n + 1} } \right)

\]

[/tex]

An advice pls, thx!

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# Homework Help: Some sums, don't sum up

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