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A partial sum is the sum of the first $n$ terms in a sequence. It provides an approximation to the sum of an infinite series.
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Infinite Series: A sum of infinitely many terms, written as $\sum_{k=1}^{\infty} a_k$. Convergence depends on the behavior of its partial sums.
Convergence: A property of an infinite series where its partial sums approach a finite limit.
Geometric Series: A series with a constant ratio between successive terms, expressed as $\sum_{k=0}^{\infty} ar^k$.