absolute convergence of double series
Let us consider the double series
Theorem. All row series, all column series and the diagonal series converge absolutely and
if one of the following conditions is true:
The diagonal series converges absolutely.
There exists a positive number such that every finite sum of the numbers is .
The row series converge absolutely and the series with
is convergent. An analogical condition may be formulated for the column series .
Example. Does the double series
converge? If yes, determine its sum.
equalling simply and having the limit as . Consequently, the given double series converges and its sum is .
|Title||absolute convergence of double series|
|Date of creation||2013-03-22 18:46:45|
|Last modified on||2013-03-22 18:46:45|
|Last modified by||pahio (2872)|