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We prove that the following three conditions together imply the concavity of the sequence $ \left\{\sum \limits_{i = 0}^n \alpha _i\beta _i / \sum \limits_{i = 0}^n\alpha _i\right\}$ : concavity of $ \{\beta _n\} $ , log-concavity of $ \{\alpha _n\} $ and nonincreasing of $ \{(\beta _n - \beta _{n-1}) / (\alpha _{n-1} / \alpha _n-\alpha _{n-2}/ \alpha _{n-1})\}$ . As a consequence we get necessary and sufficient conditions for the concavity of the sequences { S n - 1 ( x) / S n ( x)} and { S n ' ( x) / S n ( x)} for any nonnegative x, where S n ( x) is the nth partial sum of a power series with arbitrary positive coefficients { a n }. [ABSTRACT FROM AUTHOR]