Convergent Series
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 afinite number of terms from the beginning of a series. Constant terms in the denominator of a sequence can usually bedeleted without affecting convergence. All but the highest Power terms in Polynomials canusually be deleted in both Numerator and Denominator of a Series without affecting convergence. If aSeries converges absolutely, then it converges. See also Convergence Tests, Radius of Convergence
References
Bromwich, T. J. I'a. and MacRobert, T. M. An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, 1991.
- Mertens Constant
- Mertens Function
- Mertens Theorem
- Mertz Apodization Function
- Mesh Size
- Mesokurtic
- M-Estimate
- Metabiaugmented Dodecahedron
- Metabiaugmented Hexagonal Prism
- Metabiaugmented Truncated Dodecahedron
- Metabidiminished Icosahedron
- Metabidiminished Rhombicosidodecahedron
- Metabigyrate Rhombicosidodecahedron
- Metadrome
- Metagyrate Diminished Rhombicosidodecahedron
- Metalogic
- Metamathematics
- Method
- Metric
- Metric Entropy
- Metric Equivalence Problem
- Metric Space
- Metric Tensor
- Mex
- Mex Sequence