As a battery ages, the lead on the terminals will corrode on the positive side more often than the negative. The negative terminal normally stays corrosion free. It will still need to be cleaned just like the positive terminal. Corrosion on the terminals is due to hydrogen gas being released from the acid in the battery.
When the battery terminals need maintenance, the first thing you want to do is to use some battery terminal cleaner. This will neutralize the battery acid. Then you can clean the battery terminals and apply battery terminal protector.
At this time it would be good to look at the battery date code. Most riding lawn mower batteries only last for about 3 years before they become so sulfated that the battery is no longer usable.
If the battery is getting close to 3 years old, replace it. When you do, be sure to clean the battery terminals with a wire brush to remove any corrosion. Then reinstall the battery and test it to be sure that everything is working as it should. Make sure to put some battery terminal protector on the terminals and you should be good to go.
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