Answer
$\sum_{k=1}^{100}k^2$
Work Step by Step
Writing the given sum using sigma notation means to determine the general term of the sum and the limits for the summation index:
$$1^2+2^2+3^2+\dots+100^2=\sum_{k=m}^n a_k.$$
We look for the pattern in the terms of the sum: we notice that the term on the $k$th position is written as
$$a_k=k^2.$$
The summation index $k$ goes from $1$ to $100$.
We conclude that the sum can be written using sigma notation like this:
$$1^2+2^2+3^2+\dots+100^2=\sum_{k=1}^{100}k^2.$$
