What is the effective method to rapidly increase your steemit reputation score?
Reputation on Steem blockchain is basically calculated according to total of all the Reward shares (or Rshares) of every votes associated to a;; your posts and comments. You can read a much more detailed explanation regarding Steem reputation here:
https://steemit.com/steemit/@arcange/what-is-steemit-reputation-and-how-does-it-work
So now to answer your question, if raising your reputation as quick as possible is your only concern then the fastest way to increase reputation is to simply buy votes from bid bots, voting bots, etc. That being said, i personally think we should not be too concerned about our reputation score as long as it's not on the negatives so that our posts gets hidden by Steem interfaces and usually only spammers are able to drown their reputation score to the negatives. Also, reputation score is not a good indicator of an account's popularity or engagement anyway