remainder term

Let Sn be the nth partial sum of the series  a1+a2+  with real or complex an (n=1, 2,).

  • If the series is convergent with sum S, then we call the   Rn:=S-Sn  the nth remainder term or simply remainder of the series (n=1, 2,).  Then  limnRn=0.

  • If there exists a number s such that  limn(s-Sn)=0,  then the series is convergent and its sum is s.

Title remainder term
Canonical name RemainderTerm
Date of creation 2013-03-22 14:51:02
Last modified on 2013-03-22 14:51:02
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 8
Author PrimeFan (13766)
Entry type Definition
Classification msc 40-00
Synonym remainder
Synonym tail of series
Related topic SumOfSeries