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1.34 Infinite Series

An infinite series of real numbers is an array

a1+a2+a3+a_{1}+a_{2}+a_{3}+\dots

which may continue indefinitely. We write n=1an\sum_{n=1}^{\infty}a_{n}, without presupposing that the series converges. (A series involves a sum of terms, whereas a sequence is simply a list.)

Example

The series

e=1+1+12!+13!++1n!+e=1+1+{{1}\over{2!}}+{{1}\over{3!}}+\dots+{{1}\over{n!}}+\dots

defines Euler’s number ee as in 2.18.