Question

\[(a_{n})_{n\geq1}\] is a sequence of real numbers , when is a \[\sum_{n=1}^{\infty}a_{n}\] converged ?

Answer 1

\[\sum_{n=1}^{\infty}a_n\]?

Answer 2

yes it is sorry for writing wrong

Answer 3

not a simple question to answer
the definition is it converges with
\[\lim_{n\to \infty}\sum_{k=1}^na_n\] exists
i.e. when the limit of the partial sums exists
there are numerous tests to check if that limit exists or not

Answer 4

ok..

Answer 5

there are (small) books on summing series, it is not a topic finished in a chat box

Answer 6

ok, maybe i translated wrong the question, actually its a question of our professor in our last exam and i think it should have an answer but as i said my translation is maybe weak