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June 17th, 2018, 03:39 AM   #1
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infinite series

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3/13+33/13^2+333/13^3+3333/13^4+....
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June 17th, 2018, 05:35 AM   #2
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write the series as

$\displaystyle \sum \limits_{k=1} \dfrac{10^k-1}{3\cdot 13^k}$

this is then the scaled difference of two geometric series whose values should be easy enough to compute.
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