Noun
infinite series (plural infinite series)
(mathematical analysis) Any expression that represents the addition a countably infinite number of ordered summands, often explicitly indexed by the positive or nonnegative integers.
In 1734, Leonhard Euler solved the Basel problem by summing the infinite series
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{\displaystyle \textstyle {\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots =\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {\pi ^{2}}{6}}}
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In the order of literature, as in others, there is no act that is not the coronation of an infinite series of causes and the source of an infinite series of effects. Jorge Luis Borges
We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind. Gottfried Leibniz
It is clear to all that the animal organism is a highly complex system consisting of an almost infinite series of parts connected both with one another and, as a total complex, with the surrounding world, with which it is in a state of equilibrium. Ivan Pavlov
The scheme: shell companies controlled by in turn by other shall companies based offshore, run by legal firms through trusts, in an infinite series of steps that make it impossible to track down the true account holder. Roberto Saviano
In the universe there is room for an infinite series of beginnings. Celia Green
Euler needed it to compute slowly converging infinite series while Maclaurin used it to calculate integrals. Source: Internet