<s>[INST] Expression generating $\left( \frac{3}{10}, \, \frac{3}{10} + \frac{33}{100}, \, \frac{3}{10} + \frac{33}{100} + \frac{333}{1000}, \dots \right)$ I'm looking for a closed-form expression (in terms of $n$), that will give the sequence
$$
(s_n) = \left( \frac{3}{10}, \, \frac{3}{10} + \frac{33}{100}, \, \frac{3}{10} + \frac{33}{100} + \frac{333}{1000}, \dots \right).
$$
Can anyone think of one? I made a related post to this question several minutes ago but I realized I was interpreting the sequence wrong.
 [/INST] Built on my answer to the OP's previous post of the similar question, then:
$s_n = \displaystyle \sum_{k=1}^n \left(\dfrac{1}{3} - \dfrac{1}{3\cdot 10^k}\right)$
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