$\textbf{Convergence of a series}$
A series $\sum_{k=1}^\infty a_k$ converges to $a\in\R$ if the sequence of partial sums $(s_n)_{n\in\N}$ converges to $a$.
Note: If a series converges, the symbol $\sum_{k=1}^\infty a_k$ is often used both for the series itself and the limit $a$.
$\textbf{Convergence of a series}$
A series $\sum_{k=1}^\infty a_k$ converges to $a\in\R$ if the sequence of partial sums $(s_n)_{n\in\N}$ converges to $a$.
Note: If a series converges, the symbol $\sum_{k=1}^\infty a_k$ is often used both for the series itself and the limit $a$.
copied
𝐂𝐨𝐧𝐯𝐞𝐫𝐠𝐞𝐧𝐜𝐞 𝐨𝐟 𝐚 𝐬𝐞𝐫𝐢𝐞𝐬
A series ∑ₖ₌₁ ᪲ 𝑎ₖ converges to 𝑎∈ℝ if the sequence of partial sums (𝑠ₙ)ₙ∈ℕ converges to 𝑎.
Note: If a series converges, the symbol ∑ₖ₌₁ ᪲ 𝑎ₖ is often used both for the series itself and the limit 𝑎.