In many CAS-systems, one can sum a sequence of numbers using the syntax
  sum(a(k), k, kStart, kEnd) for a sequence a(k) (of real and integer values) with the variable k.

What's the best and fastest way to do this with LaTeX?

For example, when you want to calculate thousands of values ​​for a table.

I've developed a MWE using foreach and fpeval.

\documentclass[margin=5pt, varwidth]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand\Sum[4]{%
\def\mysum{0}%
\foreach #2 in {#3,...,#4}{% 
   \def\psum{\fpeval{(#1)}}%
   \xdef\mysum{\fpeval{\mysum+\psum}}%
}\mysum}

\begin{document}
Test 1: $\displaystyle\sum\limits_{k=1}^{100} k = \Sum{\k}{\k}{1}{100}$

\newcommand\binomial[2]{\fpeval{fact(#1)/(fact(#2)*fact(#1-#2))}}
Test 2: $\displaystyle\sum\limits_{k=0}^{5} \dbinom{5}{k}
= \Sum{  \binomial{5}{\k}  }{\k}{0}{5} =2^5 = \fpeval{2^5}$
\end{document}

In many computer algebra systems, one can sum a sequence of numbers using the syntax sum(a(k), k, kStart, kEnd) for a sequence a(k) (of real and integer values) with the variable k.

What's the best and fastest way to do this with LaTeX?

For example, when you want to calculate thousands of values ​​for a table.

I've developed a MWE using foreach and fpeval.

\documentclass[margin=5pt, varwidth]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand\Sum[4]{%
\def\mysum{0}%
\foreach #2 in {#3,...,#4}{% 
   \def\psum{\fpeval{(#1)}}%
   \xdef\mysum{\fpeval{\mysum+\psum}}%
}\mysum}

\begin{document}
Test 1: $\displaystyle\sum\limits_{k=1}^{100} k = \Sum{\k}{\k}{1}{100}$

\newcommand\binomial[2]{\fpeval{fact(#1)/(fact(#2)*fact(#1-#2))}}
Test 2: $\displaystyle\sum\limits_{k=0}^{5} \dbinom{5}{k}
= \Sum{  \binomial{5}{\k}  }{\k}{0}{5} =2^5 = \fpeval{2^5}$
\end{document}

In many CAS-systems, one can sum a sequence of numbers using the syntax
sum(a(k), k, kStart, kEnd) for a sequence a(k) with the variable k.

What's the best and fastest way to do this with LaTeX?

For example, when you want to calculate thousands of values ​​for a table.

I've developed a MWE using foreach and fpeval.

\documentclass[margin=5pt, varwidth]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand\Sum[4]{%
\def\mysum{0}%
\foreach #2 in {#3,...,#4}{% 
   \def\psum{\fpeval{(#1)}}%
   \xdef\mysum{\fpeval{\mysum+\psum}}%
}\mysum}

\begin{document}
Test 1: $\displaystyle\sum\limits_{k=1}^{100} k = \Sum{\k}{\k}{1}{100}$

\newcommand\binomial[2]{\fpeval{fact(#1)/(fact(#2)*fact(#1-#2))}}
Test 2: $\displaystyle\sum\limits_{k=0}^{5} \dbinom{5}{k}
= \Sum{  \binomial{5}{\k}  }{\k}{0}{5} =2^5 = \fpeval{2^5}$
\end{document}

In many CAS-systems, one can sum a sequence of numbers using the syntax
sum(a(k), k, kStart, kEnd) for a sequence a(k) (of real and integer values) with the variable k.

What's the best and fastest way to do this with LaTeX?

For example, when you want to calculate thousands of values ​​for a table.

I've developed a MWE using foreach and fpeval.

\documentclass[margin=5pt, varwidth]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand\Sum[4]{%
\def\mysum{0}%
\foreach #2 in {#3,...,#4}{% 
   \def\psum{\fpeval{(#1)}}%
   \xdef\mysum{\fpeval{\mysum+\psum}}%
}\mysum}

\begin{document}
Test 1: $\displaystyle\sum\limits_{k=1}^{100} k = \Sum{\k}{\k}{1}{100}$

\newcommand\binomial[2]{\fpeval{fact(#1)/(fact(#2)*fact(#1-#2))}}
Test 2: $\displaystyle\sum\limits_{k=0}^{5} \dbinom{5}{k}
= \Sum{  \binomial{5}{\k}  }{\k}{0}{5} =2^5 = \fpeval{2^5}$
\end{document}