In this paper, we consider a dual-hop wireless cooperative network with amplify-and-forward (AF) relaying. The output signal-to-noise ratio (SNR) at the destination of the AF cooperative networks is in the form of the sum of harmonic mean of the source-relay channel SNR and the relay-destination channel SNR. Instead of deriving the exact probability density function (PDF) of the output SNR, we study the series expansion of this PDF around zero. This result is then applied to evaluate the performance of the AF cooperative systems over Nakagami-m fading channels, and closed-form high-SNR approximations of the average symbol error rate (SER) and the outage probability are derived. Next, we investigate the optimal power allocation (OPA) among the source node and the relays to minimize the approximate SER as well as the outage probability. It is shown that the optimal power allocation depends on the channel mparameters and the ratio of the source-relay channel gain to the relay-destination gain. In addition to the optimal power allocation, we also propose a low complexity sub-optimal power allocation (SubOPA) scheme. The performance improvement with optimal and sub-optimal power allocation is analyzed and validated by numeric results. It is shown that equal power allocation is near optimal when the relays are close to the source, while significant performance improvement is observed by both the optimal and sub-optimal power allocation schemes when the relays are close to the destination.