Hello,
If is a diverging series, is equal to zero, or is it undefined?
That is a case where You must be carefull!... if diverges, the following expressions are not the same...
a)
b)
In a) each term of the 'sum' is a divergent series and the 'sum' is impossible. In b) You have a single series with all terms equal to 0, so that it converges and its sum is 0...
Kind regards