SMO Open · 3. Polynomials, functional equations and sequences
Sum sequences by telescoping, find periods and limits of recurrences, use roots and Vieta for polynomials, and solve functional equations by well-chosen substitutions.
Sum arithmetic, geometric and telescoping sequences correctly.
Find the period or the limit of a sequence given by a recurrence.
Use the factor theorem and a helper polynomial to find unknown values.
Move between power sums of roots and Vieta coefficients.
Solve functional equations by substitutions and justify that the answer is complete.