Date: January 4 2021
Summary: A brief overview on what arithmetic series are and some of its underlying math.
Keywords: ##zettel #arithmetic #sums #series #proof #archive
An arithmetic sequence is one which the difference between one term and the next only differs by a constant. One example is this:
where the difference between each proceeding term is the constant value, 1.
An arithmetic series is one in which values in an arithmetic sequence are summed together:
This is a visual proof of the Arithmetic Series algorithm:
A formalization of the above is:
which is equivalent to:
The latter formalization is somewhat more common and it works as gives the same values as what the size of the sequence is which is . From the visual proof, the constant comes from halving the size of each region.
(Thanks to Mark Kittisopikul, Yingbo Ma, and Benoit Pasquier for these explanations)
Zelko, Jacob. Arithmetic Sums & Series. https://jacobzelko.com/01052021044121-arithmetic-series. January 4 2021.