What is the sum that can be asked?

The mixture of arithmetic series and geometric series and complex point addition 1 2+2 2+3 3+...+N 2 or cubic summation are all within your knowledge.

2. Cumulative method An/A(n- 1)=f(n)

Where f(n) needs to be the same as the accumulation method (where f(n) is arithmetic progression or geometric progression or other requirements)?

In the case of accumulation method, f(n) is generally clever and flexible, such as an/a (n-1) = (n-1)/(n+1), and there is basically no possibility that f(n) similar to accumulation method is arithmetic progression or geometric series or other sums.