Final answer:
A port scanner is the correct tool for checking a network for services such as FTP or Telnet running on servers; it probes for open ports indicating active services.
Step-by-step explanation:
To check a network for services such as File Transfer Protocol (FTP) or Telnet running on servers, you would use a port scanner. A port scanner is a tool that probes a server or host for open ports. These open ports signify the presence of active services, such as FTP, Telnet, web servers, and other applications that might be running on a server. Port scanners can help network administrators identify open ports that are accessible on the network, assess security policies, and audit the network for potential vulnerabilities.
A tool like a packet sniffer can capture and analyze network traffic but is not specifically designed to locate services on a set of ports. A syslog server is a centralized logging system that collects and stores logs from various network devices but does not actively probe for open ports or running services. A Network Intrusion Detection System (NIDS) is used to monitor the network for malicious activities or policy violations, again, it does not solely focus on identifying running services.