# Difference between revisions of "Harmonic series"

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The alternating harmonic series, | The alternating harmonic series, | ||

− | <math>\displaystyle\sum_{i=1}^{\infty}\frac{(-1)^{i+1}}{i}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots</math> , though approaches <math> \ln 2</math>. | + | <math>\displaystyle\sum_{i=1}^{\infty}\frac{(-1)^{i+1}}{i}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots</math> , though, approaches <math> \ln 2</math>. |

− | The general harmonic series, <math>\displaystyle\sum_{i=1}^{\infty}\frac{1}{ai +b}</math> has its value depending on the value of the constants <math>a</math> and <math>b</math>. | + | The general harmonic series, <math>\displaystyle\sum_{i=1}^{\infty}\frac{1}{ai +b}</math>, has its value depending on the value of the constants <math>a</math> and <math>b</math>. |

The [[zeta-function]] is a harmonic series when the input is one. | The [[zeta-function]] is a harmonic series when the input is one. | ||

== How to solve == | == How to solve == |

## Revision as of 11:59, 28 June 2006

There are several types of **harmonic series**.

The the most basic harmonic series is the infinite sum This sum slowly approaches infinity.

The alternating harmonic series, , though, approaches .

The general harmonic series, , has its value depending on the value of the constants and .

The zeta-function is a harmonic series when the input is one.