infinite series سری ِ بیکران seri-ye bikarân (#)
*Fr.: série infinie*
A series with infinitely many terms, in other words a series that has no last term, such as
1 + 1/4 + 1/9 + 1/16 + · · · + 1/*n*^{2} + ... .
The idea of infinite series is familiar from decimal expansions, for instance the expansion
π = 3.14159265358979... can be written as
π = 3 + 1/10 + 4/10^{2} + 1/10^{3} + 5/10^{4} +
9/10^{5} + 2/10^{6} + 6/10^{7} + 5/10^{8} +
3/10^{9} + 5/10^{10} + 8/10^{11} + ... ,
so π is an "infinite sum" of fractions. See also → *finite series*. → *infinite*; → *series*. |