## Infinite Series

### Sequences and Series

Sequence is a succession of numbers formed according to some fixed rule. Example is

$1,~ 8,~ 27,~ 64,~ 125,~ ...$

which is a sequence so that the n^{th} term is given by n^{3}.

Series is the indicated sum of a sequence of numbers. Thus,

$a_1 + a_2 + a_3 + ... + a_n + ...$

is the series corresponding to the sequence $a_1,~ a_2,~ a_3,~ ... ,~a_n,~ ...$

**Finite and Infinite Series**

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