Let n and m be natural numbers. Suppose that { a i } i = 1 n + m is an increasing, logarithmically convex, and positive sequence. Denote the power mean P n ( r ) for any given positive real number r by P n ( r ) = ( ( 1 / n ) ∑ i = 1 n a i r ) 1 / r . Then P n ( r ) / P n + m ( r ) ≥ a n / a n + m . The lower bound is the best possible.