Calculus

Sequences and Series

Limit of Series

The definition of limit of series is this.

$$\begin{gathered} \underset{n\to \mathrm{\infty }}{\lim }{a}_n=l⟺{ \\ }^{\mathrm{\exists }}N\in \mathbb{\mathbb{N}},{ \\ }^{\mathrm{\forall }}ϵ, \\ n>N\to |a_n-l|<ϵ \end{gathered}$$