134. Series

Provided the limit exists:

• If : limit exists

• If do not have the same sign:

  • Limit need not exists

  • Limit may exists but be different if we sum in a different order

    • Limit exists and independent of order of summation if

Geometric Series

Derivation:

Summation in series with multiple indices

If the sum of the absolute value of the terms of the series are finite,

the order in which the elements are summed will not matter

E.g.: