What is a divergent infinite series?

1 Answer
Wataru
Sep 18, 2014

The sum #S# of a series #sum_{k=1}^infty a_k# is defined as
#S=lim_{n to infty}S_n#,
where #S_n# is the nth partial sum defined as
#S_n=a_1+a_2+a_3+cdots+a_n=sum_{k=1}^na_k#.

So, a series is called divergent when the limit (the sum)

#S=lim_{n to infty}S_n#

does not exist (including infinite limits).

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