Accurate nucleus detection in pathology images is crucial for disease diagnosis. Deep learning based methods require extensive annotations of nuclei, which are time-consuming for pathologists. Active learning (AL) provides an attractive paradigm for reducing annotation efforts by iteratively selecting the most valuable samples for annotation. However, most AL methods do not consider utilizing crowdsourced annotations from multiple workers with varying expertise levels and labeling costs, limiting their practical applicability. Recent approaches design AL strategies that adaptively select the most cost-effective worker for each sample, but these methods solely focus on the classification task, overlooking the development of an AL framework with crowdsourced annotations for the detection task. Additionally, they struggle to adapt to the changes in model performance during AL iterations, resulting in inefficiencies in sample selection and cost management. Based on the above considerations, we propose C2AL, a novel cost-effective AL framework using crowdsourced annotations for nucleus detection in pathology images. Specifically, we design a new criterion in the form of score function and a dynamic weighting adjustment strategy to iteratively select the most cost-effective sample-worker pairs from the crowdsourced data. Then, based on the selected sample-worker pairs, the labeled pool is updated and the detection model is trained for performance evaluation. To the best of our knowledge, this is the first AL framework for detecting nuclei in the crowdsourced environment, and the experimental results on one real-world and two simulated crowdsourced datasets demonstrate that C2AL achieves higher detection accuracy at lower annotation costs compared to existing methods.