If the above method doesn't work, you can try downloading the Google Play Services APK file directly. Please note that this method requires enabling "Unknown Sources" on your device.
Navigating Legacy Android Ecosystems: A Technical Guide to Acquiring and Installing Google Play Services for Android 7.1.1 (Nougat) download google play services for android 7.1.1
Ensure your device has sufficient free space, as updates may fail if storage is full. Google Help Keep your device & apps working with Google Play services If the above method doesn't work, you can
Settings → Apps → Google Play Services If the above method doesn't work
Leo’s dad had given him the phone two years ago with a sigh. "It's old, son. But it still works." And it had. Until today. Until the apps decided that 7.1.1 was a ghost that no longer needed serving.