This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 1

2013 Bogdan Stan, 2
Let $ \left( a_n \right) ,\left( b_n \right) $ be two sequences of real numbers from the interval $ (-1,1) $ having the property that $$ \max\left( \left| a_{n+1} -a_n \right| ,\left| b_{n+1} -b_n \right| \right) \le\frac{1}{(n+4)(n+5)} , $$ for any natural number. Prove that $ \left| a_nb_n -a_1b_1 \right|\le 1/2, $ for any natural number $ n. $ [i]Cristinel Mortici[/i]
inequalities induction boundedness sequence algebra mathematical induction sequences triangle inequality