Series
Series
It is often important and valuable to determine the sum of the terms of an arithmetic or geometric sequence. The sum of any sequence of numbers is called a series.
Finite series
We use the symbol \({S}_{n}\) for the sum of the first \(n\) terms of a sequence \(\{{T}_{1}; {T}_{2}; {T}_{3}; \ldots;{T}_{n}\}\):
\[{S}_{n}={T}_{1}+{T}_{2}+{T}_{3}+\cdots + {T}_{n}\]If we sum only a finite number of terms, we get a finite series.
For example, consider the following sequence of numbers
\[1; 4; 9; 16; 25; 36; 49; \ldots\]We can calculate the sum of the first four terms:
\[{S}_{4}=1+4+9+16=30\]This is an example of a finite series since we are only summing four terms.
Infinite series
If we sum infinitely many terms of a sequence, we get an infinite series:
\[{S}_{\infty }={T}_{1}+{T}_{2}+{T}_{3}+ \cdots\]This lesson is part of:
Sequences and Series
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