A sequence of the form
of real or complex numbers is called geometric sequence. of the geometric sequence is thus that every two consecutive members of the sequence have the constant ratio , called usually the common ratio of the sequence (if , speaking the ratio of members does not exist).
The member of the geometric sequence has the
Let . The sequence is convergent for having the limit (http://planetmath.org/LimitOfRealNumberSequence) 0, and for having as constant sequence the limit .
When the members of the sequence are positive numbers, each member is the geometric mean of the preceding and the following member; the name “geometric sequence”(or “geometric series”) is due to this fact (a fact is true for the harmonic series and harmonic mean).
|Date of creation||2013-03-22 14:38:52|
|Last modified on||2013-03-22 14:38:52|
|Last modified by||pahio (2872)|