« Vrati se
The real numbers a_0,a_1,a_2,\ldots satisfy 1=a_0\le a_1\le a_2\le\ldots. b_1,b_2,b_3,\ldots are defined by b_n=\sum_{k=1}^n{1-{a_{k-1}\over a_k}\over\sqrt a_k}.

a.) Prove that 0\le b_n<2.

b.) Given c satisfying 0\le c<2, prove that we can find a_n so that b_n>c for all sufficiently large n.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1675IMO Shortlist 1986 problem 120
1492IMO Shortlist 1976 problem 61
1453IMO Shortlist 1973 problem 110
1403IMO Shortlist 1970 problem 21
1156IMO Shortlist 1961 problem 31
1143IMO Shortlist 1959 problem 33