My answer to this question this site has gained several upvotes and downvotes by now. That's a fresh situation for me since, generally my answer received solely upvotes or downvotes, but not both. As to this answer, I checked it carefully but found no mistakes, so I just don't understand what's the reason of these downvotings. Therefore, I'm considering to make a flag to ask the moderator for investigating the downvotings, giving explanations if there is any or cancelling the downvotings if they lack reasons. Is this an appropriate act?
Downvotes and upvotes are not solely used to judge the correctness of an answer. Indeed, the tooltips for these arrows say
This answer is useful
This answer is not useful
respectively (emphasis mine). That different users could judge the same answer to be of different utility is actually not surprising. It is certainly not something that requires moderator attention. We have no way of determining which users downvoted or upvoted that particular answer, and even if we could determine this we have no way to force those users to divulge their reasons. (We're also not mind-readers, but that should go without mention.)
Furthermore, the invalidation of votes is only done if there is pretty strong evidence that the votes were made based on something other than the (necessarily subjective) merit of the individual post, usually in the form of targeted voting of the posts of one account by another. Outside of sockpuppetry, I don't think I've ever heard of the invalidation of multiple votes for the same post (which must come from different accounts).
What to do? Pretty much what you've done so far. Look over your post to see if there is anything to improve. When you are happy with what you've submitted, move on. As Jesus once said,
It's not a big deal, but I for one would like to know why a particular answer has been downvoted. It would be helpful to know if the math is flat out wrong or the post is not clear. I have seen downvoted answers that seem clear and correct, and have had an answer of my own to a very simple problem downvoted. One wonders why.