Mathematical Analysis

Sequences and Series

What does it mean if a series is convergent?

Convergence of a series is related to the convergence of a sequence, but don’t confuse them. The convergence of the sequence of partial sums (usually written as {sn}) differs greatly from the convergence of a sequence of numbers (usually written as {xn}). For example, the series Σxn (and its associated sequence of partial sums, or {sn}), is convergent if and only if the sequence {sn} is convergent. Thus, the total sum of the series is the limit of the sequence {sn}, seen as:



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