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# Understanding the limit? trend = pattern A limit is the value at the end of the pattern. Although the pattern will continue, the exact value keeps changing, and the trend (the outcome) can be determined. This is the limit, the long-term end behavior of a pattern or trend. The symbol of limit is "...

# Understanding the limit? trend = pattern A limit is the value at the end of the pattern. Although the pattern will continue, the exact value keeps changing, and the trend (the outcome) can be determined. This is the limit, the long-term end behavior of a pattern or trend. The symbol of limit is "lim". The term "limit" is used because it describes the value that a function approaches as the input gets closer, and closer, to a certain value, but never actually reaches it. ## Example 2: Alongside infinity is the idea of limits. Think about this pattern and what comes next. The image contains several squares divided into smaller squares, with some squares highlighted in yellow. Below each square are fractions and corresponding decimal values or approximate decimals. Here's a breakdown of the pattern: | Fraction | Decimal | | --------- | -------- | | $\frac{1}{2}$ | 0.5 | | $\frac{1}{4}$ | 0.25 | | $\frac{1}{8}$ | 0.125 | | $\frac{1}{16}$ | 0.0625 | | $\frac{1}{32}$ | 0.03125 | | | 0.03| | $\frac{1}{64}$ | 0.015625 | | | 0.02 | | $\frac{1}{128}$ | 0.0078125 | | | 0.008 | | $\frac{1}{256}$ | 0.00390625 | | | 0.004 | | $\frac{1}{512}$ | 0.001953125 | | | 0.002 | |... |... |