Putnam 1994/A1 solution

Problem A1

a_n is a sequence of positive reals satisfying a_n ≤ a_2n + a_2n+1 for all n. Prove that ∑ a_n diverges.

Solution

Trivial.

∑ a_n = a₁ + (a₂ + a₃) + (a₄ + a₅ + a₆ + a₇) + ... and each bracket has sum at least a₁ > 0.