A series is the sum of the terms of a sequence. Mathematically, if we have a sequence \(a_{1}, a_{2}

Question

A series is the sum of the terms of a sequence. Mathematically, if we have a sequence $a_{1}, a_{2}, a_{3}, \dots, a_{n}$, the corresponding series is written as: $S_{n} = a_{1} + a_{2} + a_{3} + \dots + a_{n}.$ The series can be either finite (with a limited number of terms) or infinite (with terms continuing indefinitely). In general, the general term of a sequence can be expressed as: $$T_{n} = S_{n} - S_{n-1}$$ Here $T_n=S_n-S_{n-1}$ for $n\ge2$, with $T_1=S_1$. Equivalently define $S_0=0$.

Accepted Answer

$S_n=a_1+\cdots+a_n$; $T_1=S_1$, $T_n=S_n-S_{n-1}$ for $n\ge2$.

A Brief Introduction of Series

A Brief Introduction of Series

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