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 \(\frac{1}{4}-\frac{1}{9}+\frac{1}{16}-\frac{1}{25}+\text{…}\), 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 \(n\) as \(\frac{1}{n^2}\), where \(n\) starts at 2. However, since the terms alternate in sign, we introduce \( (-1)^{n+1}\), making the general term \((-1)^{n+1}\frac{1}{n^2}\). This general term helps in expressing the entire series compactly.