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Given any sequence \((a_n)_{n \in \N}\text{,}\) we can always form a new sequence \((b_n)_{n \in \N}\) by

\begin{equation*} b_n = a_0 + a_1 + a_2 + \cdots + a_n\text{.} \end{equation*}

Since the terms of \((b_n)\) are the sums of the initial part of the sequence \((a_n)\) ways call \((b_n)\) the sequence of partial sums of \((a_n)\). Soon we will see that it is sometimes possible to find a closed formula for \((b_n)\) from the closed formula for \((a_n)\text{.}\)

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