# convergence of a series

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__Convergence of a Series
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__Convergence of a Series
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In other words a sequence in a set S is a rule which assigns to each natural number a unique element of S.

A sequence whose range is a subset of R is called a real sequence or a sequence of real numbers.

In this question we will solve and study only real sequences. therefore the term sequence will be used to denote a real sequence.

If s is a sequence,then the image ss(n) of N is usually denoted by s(n). It is customary to denote the sequence s by the symbol <s(n)>.The image s(n) of n is called the nth term of the sequence.

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convergence of a series |

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2.__A sequence(series) can be described in several different ways__–

__A sequence(series) can be described in several different ways__

(1.)Listing in order the first few elements of a sequence,till the rule for writing down different elements becomes clear.For example,<1,8,27,64,…>is the sequence.

(2.)Defining a sequence by a formula for its nth term.For example,the sequence <1,8,27,64,….> can also be written as <1,8,27,…..,n^3,…..>