[Tex/LaTex] Nested Summation

Question

Using below code i am getting result shown in below image but its not properly displayed
for

1. ex space on either side of =.
2. First summation sign is small.
3. Brackets ( ) are small.
4. All items are not placed properly with spaces between them.

How to improve all these things?

T(n)= $\sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1)$ 

MWE

\documentclass{article}

\usepackage{fancyhdr} % Required for custom headers
\usepackage{lastpage} % Required to determine the last page for the footer
\usepackage{extramarks} % Required for headers and footers
\usepackage[usenames,dvipsnames]{color} % Required for custom colors
\usepackage{graphicx} % Required to insert images
\usepackage{listings} % Required for insertion of code
\usepackage{courier} % Required for the courier font
\usepackage{lipsum} % Used for inserting dummy 'Lorem ipsum' text into the template
\usepackage{mathtools}          %loads amsmath as well
\DeclarePairedDelimiter\Floor\lfloor\rfloor
\DeclarePairedDelimiter\Ceil\lceil\rceil

% Margins
\topmargin=-0.45in
\evensidemargin=0in
\oddsidemargin=0in
\textwidth=6.5in
\textheight=9.0in
\headsep=0.25in

\linespread{1.1} % Line spacing
\begin{document}
\section{eqn}
 T(n)= $\sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1)$
\end{document}

Answer 1

There is a bunch of options to improve this:

• Put T(n) in math mode --> spacing before = is better
• Use \left(....\right) to get bigger bracket, however the spacing before and after brackets are too large
• Use \biggl(...\biggr) for larger brackets and better spacing
• Use \mleft( and \mright) from the mleftright package for adapted brackets and better spacing

The output of those options can be seen from the screen shot

---

\documentclass{article}

\usepackage{fancyhdr} % Required for custom headers
\usepackage{lastpage} % Required to determine the last page for the footer
\usepackage{extramarks} % Required for headers and footers
\usepackage[usenames,dvipsnames]{color} % Required for custom colors
\usepackage{graphicx} % Required to insert images
\usepackage{listings} % Required for insertion of code
\usepackage{courier} % Required for the courier font
\usepackage{lipsum} % Used for inserting dummy 'Lorem ipsum' text into the template
\usepackage{mathtools}          %loads amsmath as well
\usepackage{mleftright}

\DeclarePairedDelimiter\Floor\lfloor\rfloor
\DeclarePairedDelimiter\Ceil\lceil\rceil

% Margins
\topmargin=-0.45in
\evensidemargin=0in
\oddsidemargin=0in
\textwidth=6.5in
\textheight=9.0in
\headsep=0.25in

\linespread{1.1} % Line spacing
\begin{document}
\section{eqn}

\begin{itemize}
\item original \\

 T(n)= $\sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1)$

\item Now with extra space 


$ T(n)\;= \sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1)$ 

\item With brackets improved 

 $T(n)\;= \sum\limits_{i=3}^{n-4}\left(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\right)$

\item With big brackets \texttt{biggl(} and \texttt{biggr)}

 $T(n) = \sum\limits_{i=3}^{n-4}\biggl(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\biggr)$ 


\item With brackets from mleftright package

$ T(n)= \sum\limits_{i=3}^{n-4}\mleft(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\mright)$ 

\item Displaystyle all together

\[ T(n)\;= \sum\limits_{i=3}^{n-4}\mleft(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\mright) \]


\end{itemize}

Now in an align-environment

\begin{align}
 T(n)&= \sum\limits_{i=3}^{n-4}(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1) \\
 T(n)&= \sum\limits_{i=3}^{n-4}\left(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\right) \\
 T(n)&= \sum\limits_{i=3}^{n-4}\mleft(\sum\limits_{j=4}^{n-1} 1 + \sum\limits_{k=10}^{n-3} 1\mright) 
\end{align}

\end{document}