# infinite series

## EnglishEdit

### NounEdit

infinite series ‎(plural infinite series)

1. (analysis) A sum with a countably infinite number of ordered summands; the sum itself is formally defined as the limit of the partial sums, if it exists.
${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots ={\frac {\pi ^{2}}{6}}}$