LaTeX: How to adjust how the Sum symbol turns out

Question

Not sure if LaTeX counts as programming, or if my question even makes sense, but I have this LaTeX expression (or what you call it):

\sum_{k=1}^n k^2 = 1+4+9+\ldots +n^2 =
\frac{1}{3}n^3 + \frac{1}{2}n^2 + \frac{1}{6}n

The problem is that the k=1 and n comes next to, i.e. after, the sum symbol, instead of above and below it. Is there a way I can change this? I have tried to show visually what I mean below. The sum symbol represented as Xs :

 n
XXX          XXX n
XXX    vs    XXX
XXX          XXX k=1
k=1

I want the first kind, but am getting the second.

Answer 1

I think you will need to use the equation environment for that:

\begin{equation}
\sum_{k=1}^n k^2 = 1+4+9+\ldots +n^2 = \frac{1}{3}n^3 + \frac{1}{2}n^2 + \frac{1}{6}n
\end{equation}

Answer 2

Try

\sum\limits_{k=1}^n k^2

if you want the sum limits to appear above and below the sum sign in an inline equation.

Answer 3

A more general solution to force a formula that is appearing in inline style to appear in display style is to start the formula with a \displaystyle declaration, e.g.

$\displaystyle \sum_{k=1}^n k^2$

This will work for any expression that appears differently in inline and display environments, such as \frac, \int, \lim, etc. You can also control the scope of the \displaystyle command by enclosing the desired expression in braces. For example, if you want the sum in your example formula to appear in display style but not the fractions, you could use

${\displaystyle \sum_{k=1}^n k^2} = 1+4+9+\ldots +n^2 = 
\frac{1}{3}n^3 + \frac{1}{2}n^2 + \frac{1}{6}n$