toán học tuổi trẻ số 405

[...]... that does not exceed x TlO/40S Find all functions/: N' -+N' which satisfy the following conditions i) f is strictly increasing; ii) f(f(n» = 4n + 9 for all n e N'; iii) f(f(n)-n)=2n+9 for all ne N' f 8 /405 a) Find all distinct permutations of the word TOANHOCTUOITRE b) How many permutations are there that has three consecutive T - TIT? n~2sothat c) How many permutations are there without is a perfect... circumcircle of triangle APK cuts the circle (0 ) at a second point E AE cuts BC at M A 'P cuts tbe circle (0) at a second point N Prove that the line MN passes through a fixed point \, \ rv I lPI\1l 19 /405 Let k be a positive integer, a is arbitrary real number Find the limit sequence (a.) where a, = 1 aJ [2 k.aJ + ,+ [n aJ _ + (n -1,2, ), [ll n h1 Giai Ihieu SACH Tll/40S Does there exist a positive