Definition:Series/Sequence of Partial Sums

Definition

Let $\sequence {a_n}$ be a sequence in a structure $S$.

Let $s$ be the series:

$\ds s = \sum_{n \mathop = 1}^\infty a_n = a_1 + a_2 + a_3 + \cdots$

The sequence $\sequence {s_N}$ defined as the indexed summation:

$\ds s_N: = \sum_{n \mathop = 1}^N a_n = a_1 + a_2 + a_3 + \cdots + a_N$

is the sequence of partial sums of the series $\ds \sum_{n \mathop = 1}^\infty a_n$.

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 4.3$. Series
• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 6.1$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): partial sum
• 1992: Larry C. Andrews: Special Functions of Mathematics for Engineers (2nd ed.) ... (previous) ... (next): $\S 1.2$: Infinite Series of Constants
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): convergent series
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): partial sum
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): convergent series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): partial sum
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): partial sum