Although it has many solutions, it is mainly to cultivate your ability to discover the general law of series and guess the general term of series (that is, the ability to use incomplete induction).
So that when we encounter some series whose general term is difficult to find by general methods, we can guess the general term formula of this series quickly and accurately through the first few terms.
Then prove it by mathematical induction or reduction to absurdity or other methods, bypass the front mountain and quickly get its general formula (generally obtained by mathematical induction). Therefore, finding the rules to fill in the blanks will still help us to enhance our understanding of some difficulties and characteristic series.