Subjects algebra

Smallest Term

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Smallest Term


1. **Problem Statement:** Find the smallest term of the expression $$\frac{2^2}{n^2}$$ where $n$ is a variable. 2. **Rewrite the expression:** The expression simplifies as $$\frac{2^2}{n^2} = \frac{4}{n^2}$$. 3. **Analyze the expression:** Since $4$ is a constant numerator, the value of the entire fraction depends on the denominator $n^2$. 4. **Minimizing the term:** The smallest term refers to the minimum value of $$\frac{4}{n^2}$$. Because $$n^2$$ is always positive, to minimize $$\frac{4}{n^2}$$, we need to maximize $$n^2$$ (make the denominator as large as possible). 5. **Range for $n$:** Usually, $n$ is an integer or real number except zero since division by zero is undefined. 6. **Evaluating smallest value:** As $$|n|$$ approaches infinity, $$n^2$$ becomes very large, so $$\frac{4}{n^2}$$ approaches zero. 7. **Conclusion:** The smallest term or minimum value of $$\frac{4}{n^2}$$ is **0**, which is approached but never reached because $$n$$ cannot be infinite. **Final answer:** The smallest term of the expression $$\frac{4}{n^2}$$ is $$0$$ in the limit as $$|n| \to \infty$$.