Answer
$\sum\limits_{k=1}^{6}{{{k}^{2}}}$.
Work Step by Step
$1+4+9+16+25+36$
This can be written as,
${{\left( 1 \right)}^{2}}+{{\left( 2 \right)}^{2}}+{{\left( 3 \right)}^{2}}+{{\left( 4 \right)}^{2}}+{{\left( 5 \right)}^{2}}+{{\left( 6 \right)}^{2}}$
In sum the value of $k$ varies from $1$ to $6$.
Hence, the sigma notation is,
$\sum\limits_{k=1}^{6}{{{k}^{2}}}$
Thus, the sigma notation for the sum $1+4+9+16+25+36$ is$\sum\limits_{k=1}^{6}{{{k}^{2}}}$.
