As you know, in the field of education, in connection with moral education and improving the quality of education, certain events and various competitions are held on a planned basis, one of which is the annual periodic olympiads. We know that in mathematics, special attention is paid to solving problems, so the work done by students during the olympiad is largely evaluated by how well they fit into solving problems. Taking this into account, the article considers ways to confirm some properties of the Fibonacci series using the method of mathematical induction, as well as problems encountered at olympiads over the past five years on this topic, as well as methods for solving them. The considered problems can help school teachers in solving olympiad problems in mathematics.