# History Of Infinite Series

What is a good source for the history of infinite series?

Moreover, why do we learn them?

Are they really useful on their own, or are just tools / stepping stone for studying series of functions later?

• – Mark Fantini Sep 20 '14 at 9:52
• Thank you Mark Fantini – Vagabond Sep 25 '14 at 9:32
• Does the history of infinite series converge? – rbp Oct 13 '14 at 13:25
• The references I cited in my comment to the math StackExchange question References for mathematical theory of summability of divergent series might provide some useful references to the history you're looking for. – Dave L Renfro Oct 13 '14 at 17:58
• When you use your calculator to calculate a function like a sine or an exponential, it's calculating it using a series. – Ben Crowell Oct 17 '14 at 19:04

• Euclid (~300 BC) found the geometric series $\sum 1/r^n$ useful, and contemporary applications would have included Archimedes's quadrature of the parabola and for Zeno's paradoxes.
• Oresme (~1350) found the harmonic series $\sum 1/n$ useful, as an example of a divergent sum.
• Mercator (1668) found $\sum \pm\, x^n/n$ as a useful series for calculating logarithms $\log(1+x)$.