Summation symbol and fraction in LaTeX

The expressions of fraction containing a summation in the display and inline modes are slightly different like the below.

\[
\frac{ \sum_{k=1}^{n} k^2 }{ 5 }
\]
$\frac{ \sum_{k=1}^{n} k^2 }{ 5 }$

In the inline equation, the subscript of summation is so close to the fraction bar. The display styles of sum and frac make an equation more beautiful. From the below example, making both frac and sum displaystyle may be a good way if you want a denominator to look larger.

\[
\frac{ \displaystyle\sum_{k=1}^{n} k^2 }{ 5 }
\]
$\frac{ \displaystyle\sum_{k=1}^{n} k^2 }{ 5 }$ \\[15pt]
$\displaystyle\frac{ \displaystyle\sum_{k=1}^{n} k^2 }{ 5 }$

Fraction in summation

\[
\sum_{k=1}^{n} \frac{ k^2 }{ 5 }
\]
$\sum_{k=1}^{n} \frac{ k^2 }{ 5 }$ \\[15pt]
$\displaystyle\sum_{k=1}^{n} \frac{ k^2 }{ 5 }$ \\[15pt]
$\displaystyle\sum_{k=1}^{n} \displaystyle\frac{ k^2 }{ 5 }$