Question

Howdo you test for convergence and divergence and what does it mean to be conditional or absolute?

Answer 1

conditional or absolute convergence exist only in alternate series

Answer 2

There are many convergence tests.

Answer 3

A series converges absolutely when \[\sum_{}^{}|a _{k}|\] converges.

Answer 4

1) divergent test
2) integral test
3) root test
4) ratio test

Answer 5

\[\sum_{n=1}^{\infty}n/(2n+3)\] for example

Answer 6

It diverges, read about the harmonic series.

Answer 7

\[\lim_{n \rightarrow \infty}\frac{n}{2n+3}=\frac{1}{2}\]
so the series diverges.

Answer 8

\[\lim_{n \rightarrow \infty}a _{n}=0\] is a necessary property.

Answer 9

Depending on the series you will need to use different convergence tests. You should get a text that discusses it in detail.