The infinite Series
is convergent if the Sequence of partial sums

is convergent. Conversely, a Series is divergent if the Sequence of partial sums is divergent. If and are convergent Series, then and are convergent. If , then and both converge or both diverge. Convergence and divergence are unaffected by deleting a finite number of terms from the beginning of a series. Constant terms in the denominator of a sequence can usually be deleted without affecting convergence. All but the highest Power terms in Polynomials can usually be deleted in both Numerator and Denominator of a Series without affecting convergence. If a Series converges absolutely, then it converges.

**References**

Bromwich, T. J. I'a. and MacRobert, T. M. *An Introduction to the Theory of Infinite Series, 3rd ed.* New York: Chelsea, 1991.

© 1996-9

1999-05-26