Consider the following sequence of positive real numbers ⋯<a−2<a−1<a0<a1<a2<… infinite in both directions. For each positive integer k let bk be the least integer such that the ratio between the sum of k consecutive terms and the greatest of these k terms is less than or equal to bk(This fact occurs for any sequence of k consecutive numbers). Prove that the sequence b1,b2,b3,... coincides with the sequence 1,2,3,... or is eventually constant. algebranumber theoryKvant