Different types of problems have different ideas. Imagine that it is unlikely to use the same method when solving the sequence problem and the function value domain.

So I think the landlord's question is too general, and the real answer may be endless.

For example, when solving high school series problems,

General formulas for finding {an}: basic quantity method, overlapping addition, overlapping multiplication, undetermined coefficient method, logarithm, reciprocal, and whole idea. ......

General formulas for finding Sn: basic quantity method, split item elimination method, dislocation subtraction method and overall idea. ......

When solving the problem of function value domain, you can use:

Substitution method, inverse solution, stripping parameter method, combination of numbers and shapes, principal component method (using discriminant greater than or equal to zero) ......