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I wonder if anybody knows how to calculate the series below? $\sum \limits_{k=0}^\infty q^{2^k}$ if $|q|\lt1$?

Thanks a lot for answers.

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    A bit of discussion is contained on the Wikipedia page on [Lacunary series](http://en.wikipedia.org/wiki/Lacunary_function).2012-01-05
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    @Mathlover: Notice that several users have tried to improve your post (mostly by adding LaTeX for proper rendering of math symbols). You should check if we did not unintentionally change the meaning of your question and, if necessary, edit your question again.2012-01-05
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    you may want to see this paper: http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/62866/1/1090-19.pdf2012-01-05

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