ƧƿѦςɛ♏ѦਹѤʞ<p><span class="h-card" translate="no"><a href="https://social.zvavybir.eu/@zvavybir" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>zvavybir</span></a></span> <br>It does diverge. It has no sum.<br>However, the uniquely valued <a href="https://mastodon.social/tags/Riemann" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Riemann</span></a> <a href="https://mastodon.social/tags/ZetaFunction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ZetaFunction</span></a> can be analytically continued into the left half-plane where we find zeta(-1)=-1/12 (which 'looks like' 1+2+...). <a href="https://mastodon.social/tags/Ces%C3%A0ro" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Cesàro</span></a> <a href="https://mastodon.social/tags/summation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>summation</span></a> will get you part of the way there also, and, as you say, yields the same result; presumably due to some ultimate cosmic logical rightness :-) <br>I very strongly recommend BP's superb exposition of this issue<br><a href="https://www.youtube.com/watch?v=YuIIjLr6vUA" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">youtube.com/watch?v=YuIIjLr6vU</span><span class="invisible">A</span></a><br><a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>maths</span></a> <a href="https://mastodon.social/tags/AnalyticContinuation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>AnalyticContinuation</span></a> <a href="https://mastodon.social/tags/Ramanujan" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Ramanujan</span></a></p>