Answer
See below.
Work Step by Step
$S_k:2$ is a factor of $k^2-k$
$S_{k+1}:2$ is a factor of $(k+1)^2-(k+1)=k^2+2k+1-k-1=k^2+k$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.