#MathsInMinutes Day: 36 Introducing Series

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A mathematical series is an expression for the sum of the terms within a sequence. Usually indicated by the Greek letter Σ (sigma), a series can be the sum of an infinite number of terms, or of a limited range. In each case, the ranges lower and upper limits are appended below and above the Σ sign.

Given any sequence of numbers (an), the series is the infinite sum:

In many cases, this sum will tend towards infinity or it may not settle down close to a particular value. However, there are series in which the sum tends towards a single number, known as the limit. To see if a series has a meaningful limit, we define the finite partial sum Sn as the sum of the first n+1 terms, a0+a1+...an. The series will converge to a limit L of the associated sequence of a partial sums for each n tends towards L.

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