$\textbf{Series of real numbers}$
Let $(a_n)_{n\in\N}$ be a sequence of real numbers. We define a new sequence $(s_n)_{n\in\N}$ by $$s_n=\sum_{k=1}^na_k$$and call $s_n$ the $n$-th partial sum of $(a_n)_{n\in \N}$. A sequence of partial sums is called a series.
Note: A series is often denoted as $a_1+a_2+a_3+\cdots$ or $\sum_{k=1}^\infty a_k$.
$\textbf{Series of real numbers}$
Let $(a_n)_{n\in\N}$ be a sequence of real numbers. We define a new sequence $(s_n)_{n\in\N}$ by $$s_n=\sum_{k=1}^na_k$$and call $s_n$ the $n$-th partial sum of $(a_n)_{n\in \N}$. A sequence of partial sums is called a series.
Note: A series is often denoted as $a_1+a_2+a_3+\cdots$ or $\sum_{k=1}^\infty a_k$.
copied
𝐒𝐞𝐫𝐢𝐞𝐬 𝐨𝐟 𝐫𝐞𝐚𝐥 𝐧𝐮𝐦𝐛𝐞𝐫𝐬
Let (𝑎ₙ)ₙ∈ℕ be a sequence of real numbers. We define a new sequence (𝑠ₙ)ₙ∈ℕ by
𝑠ₙ=∑ₖ₌₁ⁿ𝑎ₖ
and call 𝑠ₙ the 𝑛-th partial sum of (𝑎ₙ)ₙ∈ℕ. A sequence of partial sums is called a series.
Note: A series is often denoted as 𝑎₁+𝑎₂+𝑎₃+⋯ or ∑ₖ₌₁ ᪲ 𝑎ₖ.