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For something closer to a closed formula, we could write

\begin{equation*} b_n = a_1 + a_2 + a_3 + \cdots + a_n\text{,} \end{equation*}

or the same thing using summation notation:

\begin{equation*} b_n = \sum_{i=1}^n a_i\text{.} \end{equation*}

However, note that these are not really closed formulas since even if we had a formula for \(a_n\text{,}\) we would still have an increasing number of computations to do as \(n\) increases.

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