Question in discrete mathematics *

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I have question. Can anyone able to explain to me this problem why if we have 5x the generating function $1+x^5+x^{10}+x^{15} + \ldots$ we have 5 is just constant and multiply with $x$ I know that $x$ we can write as geometric series but how we get this generating function just from information given is $5x$ but how we change 5x to this series this part i want explain thanks

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This is just the series for $\frac{1}{1 - x^5}$.