Question

what is condition for convergence and divergence of alternating series?

Answer 1

Diverges goes to zero and converges goes to infinity

Answer 2

what is condition?

Answer 3

when n goes to infinity

Answer 4

What do you mean by that?

Answer 5

Suppose you have an alternating series \[b_n=\sum (-1)^n a_n\]where \(a_n\) is another sequence. If \(a_n\) approaches 0 as \(n\) goes to infinity, then \(b_n\) also converges.

Answer 6

Also, \(a_n\) has to satisfy:\[a_{n+1} \le a_n\]right?

Answer 7

That's just if it's monotonic. It's not necessary, but it tells us more about the sequence.

Answer 8

Makes sense, thanks for the explanation :-)