Problem: Find the sum of the series

Solution: This series essentially features only parts of the form c^k and thus we should be able to transform it into a geometric series.

Since q = −3/4 satisfies |q| < 1, it follows that this series converges. To find its sum we either use the more general formula (for indexing not beginning at 0) or we first fix indexing so that it starts at 0, which can be done for instance using substitution and then factoring out (an experienced series warrior would simply factor out the first term in the series).

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