finite series seri-ye karânmand (#) Fr.: série finie A sum a_{1} + a_{2} + a_{3} + · · · + a_{N}, where the a_{i}'s are real numbers. In terms of Σ-notation, it is written as a_{1} + a_{2} + a_{3} + · · · + a_{N} = Σ (n = 1 to N). See also → infinite series. |
infinite series 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. |