Identifying the general term of a series is critical to its representation. A general term describes each term in a sequence using a simple formula. For instance, in the series , we notice the following:
- The denominators are squares of consecutive integers starting from 2: \4=2^2,\text{ }9=3^2, \text{ }16=4^2,\text{ }25=5^2 \text{…}\
- The signs alternate between positive and negative.
So, the general term can be expressed using as , where starts at 2. However, since the terms alternate in sign, we introduce , making the general term . This general term helps in expressing the entire series compactly.